Millican Colloquium Lecture Series | Department of Mathematics

# Millican Colloquium Lecture Series

Millican Lectures are made possible through the generosity of Mr. Olin Moore Millican (1904 - 1999) who established the Roy McLeod Millican Memorial Fund (an endowment) in honor of his brother.

# Spring 2011

Monday, January 24, 2011
David Vogan (Massachusetts Intstitute of Technology)
Title: The Character Table for E-8 or How We Wrote Down a 453, 60 x 453,060 Matrix and Found Happiness
Abstract: "This is a story about what happens when pure mathematicians, proud of their inability to add, try to do a really large computation. I'll explain something about what character tables for Lie groups look like, what interesting information is inside them, and how 'we' (that is, Jeff Adams and Fokko du Cloux) went about this computation."

# Fall 2010

December 6, 2010
Yiannis Moschovakis (UCLA & University of Athens, Greece)
Title: A Church-Turing Thesis for Complexity
Abstract: The Euclidean algorithm computes the greatest common divisor of two numbers a, b and decides whether they are coprime using no more than 2log(min(a,b)) divisions and no other operations. It is not known whether it is optimal, and the question is apparently quite difficult.Part of my aim in this talk is to formulate, explain and justify a general postulate about algorithms from specified primitives (like the Euclidean), which makes it possible in some cases to derive lower complexity bounds that apply to all algorithms that decide a specific relation from specified primitives. This Embedding Principle is different in form but has the same intent for complexity as that of the classical Church-Turing Thesis for computability, which is used to establish absolute undecidability results.
I will also discuss several specific lower bound results obtained by this method, for arithmetical relations like coprimeness, being a perfect square or square-free, etc., from various primitives. This work is joint with Lou van den Dries.

November 29, 2010
Volker Mayer (University of Lille, France)
Title: Harmonic analysis on reductive, p-adic groups
Abstract: Holomorphic motions arise naturally in many situations involving complex dynamical systems and are a powerful tool. For example, it has been used by M. Urbanski and A. Zdunik to give a new proof of the real analytic dependence of the Hausdorff dimension of hyperbolic Julia sets (the original approach of Ruelle uses dynamical zeta-functions).
I will review the concept of holomorphic motions and some applications to holomorphic dynamics. Then I will consider random dynamical systems and present a version of holomorphic motion of hyperbolic random Julia sets. This is part of actual work with B. Skorulski and M. Urbanski.

November 8, 2010

Viktor Levandovskyy (RWTH Aachen University, Germany)
Title: Non-commutative Groebner technology, its implementation and applications
Abstract: In this talk we give an overview of an important part of computer algebra, relying on the concept of Groebner basis. This concept exists in very general settings, including the one of free associative algebras over a fixed field. We will define a nice category of so-called G-algebras, demonstrate their properties and introduce Groebner bases for them. The notion of Gel'fand-Kirillov dimension will be introduced, as well as the algorithm for its computation. A special attention will be paid to the nice homological properties of such algebras.
A particular application is the computation of the preimage of a left ideal under a morphism of two G-algebras, which relies heavily on Groebner technology.
We will show the implementation of Groebner technology for different classes of non-commutative algebras in a computer algebra system SINGULAR (www.singular.uni-kl.de, note that it is freely available) and perform some computations live.
If the time allows, we can discuss several ongoing projects concerning algebraic analysis and D-modules, homological algebra, and polynomial modeling of signals.

October 25, 2010

Loren Spice (Texas Christian University)

Title: Characters tell all: Harmonic analysis on reductive, p-adic groups

Abstract: It has been said that the 'proper' realisation of a group always involves its action by symmetries on some space. This principle manifests everywhere from geometry, to classical analysis, to number theory. Unfortunately, most symmetries are too hard to study directly, so we must usually linearise them. The study of linearised group actions is called representation theory. In the late 1960's and early 1970's, Langlands proposed a far-reaching collection of conjectures unifying algebraic, geometric, and analytic perspectives on representation theory. Much deep work has been done in the pursuit of these conjectures, but, until recently, the fundamental objects of harmonic analysis, group characters, have not been put to their full use. In this talk, we will discuss the application of character formulas to questions about stable distributions on reductive, p-adic groups.

October 11, 2010

Bentuo Zheng (University of Memphis)

Title: Game Theory and Embeddings

Abstract: In this talk, I am going to talk about some of the most important and elementary problems in Banach space theory. We will see how to use game theory to characterize subspaces of Banach spaces with unconditional bases. Recent related results and open problems will also be discussed.

September 27, 2010

Anna Zdunik (University of Warsaw)

Title: Thermodynamic formalism and dimension properties of invariant sets in the dynamics of transcendental meromorphic funcions

Abstract: In this talk I will present some recent results on dimension of invariant sets, mainly the Julia set and the "conical" Julia set appearing in the dynamics of transcendental maps. I will outline shortly the recent progress in developing the thermodynamic formalism in the context of transcendental dynamics. I will then present the strategy of the proof of Bowen's formula for the dimension of the "conical Julia set". It turns out that the formula can be proved under very mild assumptions about the map in question. Finally, I will speak about the dynamics of the "model" family of transcendental maps $\lambda\exp(z)$. I will formulate several, quite surprising results on the dimension of some invariant sets for this family.

The talk will be based on the results recently obtained in collaboration with Krzysztof Baranski and Boguslawa Karpinska.

September 13, 2010

John Clemens (UNT)

Title: Difficulty of classification problems and the isomorphism of subshifts

Abstract: A classification problem in mathematics is the problem of determining when two of a given collection of structures are appropriately equivalent. A solution of a classification problem involves providing some manner for making the determination of equivalence, such as developing a complete system of invariants. The difficulty of a classification problem can be measured by considering how complicated such invariants must be. Using descriptive set theory, we can provide a precise notion of when one classification problem is fundamentally more complicated than another, and provide a number of standard benchmarks for levels of complexity.

In this talk, I will first give an overview of this theory of Borel reducibility of equivalence relations and classification problems. I will then apply this theory to determine the complexity of the isomorphism problem for subshifts, i.e., the dynamical systems corresponding to topologically closed and shift-invariant subsets of the space of all bi-infinite sequences on a finite alphabet, considered up to shift-preserving topological isomorphism.

# Spring 2010

April 16, 2010

Stephen Griffeth (The University of Edinburgh)

Title: Orthogonal functions and representation theory

Abstract: Jack polynomials are eigenfunctions for the Calogero-Moser Hamiltonian associated to n particles on a circle interacting via inverse square potentials. The set of all n-tuples of points in the plane is a singular algebraic variety, of which the spherical subalgebra of the rational Cherednik algebra is a non-commutative deformation. More generally, one may associate a rational Cherednik algebra to each finite group generated by reflections, and it is an interesting question to decide when the full rational Cherednik algebra is Morita equivalent to its spherical subalgebra. We'll explain how to use a version of Jack polynomials to answer this question for the infinite family of complex reflection groups (and in particular for the classical Weyl groups).

This talk is based on joint work with Charles Dunkl.

Friday, April 2, 2010

Professor Lance Littlejohn (Chair, Mathematics - Baylor University)

Title: Legendre polynomials, Legendre-Stirling Numbers, and Left-Definite Operator Theory

Friday, March 5, 2010

Sergei Tabachnikov (Penn State University)

Title: Pentagrama Myrificum, Old wine into new wineskins .

Abstract: The Pentagram map is a projectively natural iteration on plane polygons. Computer experiments show that the Pentagram map has quasiperiodic behavior. I shall show that the Pentagram map is a completely integrable system whose continuous limit is the Boussinesq equation, a well known integrable system of soliton type. As a by-product, I shall demonstrate new configuration theorems of classical projective geometry.

# Fall 2009

December 11, 2009

William B. Johnson, Texas A&M University
Ten 20+ year old problems in the geometry of Banach spaces.

Monday, November 23, 2009

Volker Mayer (University of Lille, France).
Friday, November 6, 2009

Conical rigidity for Ahlfors Island mappings
An invariant line field (ILF) of a holomorphic function $f$ is a measurable field of non-oriented lines that is preserved under the action of $f$. The no invariant line field conjecture states that rational functions that are not flexible Lattes maps do not support invariant line fields. Some partial positive answers are known. In particular, McMullen showed that a rational function does not have an ILF supported on the conical limit set. This result was generalized to arbitrary transcendental meromorphic functions by Rempe and van Strien, extending earlier partial results by Graczyk, Kotus and Swiatek. These original proofs use orbifold theory and are somewhat involved.

We present a joint work with L. Rempe in which we give a very elementary proof of previously obtained results. Not only it simplifies considerably the original proofs but our approach also applies to the more general class of Ahlfors Island mappings.

Professor Dorin Andrica, Babes-Bolyai Univ. in Cluj, Romania

NEW RESULTS INVOLVING FUNCTIONS WITH MINIMAL CRITICAL SET

Abstract: Let F _ C1(Mm;Nn) be a family of smooth mappings M ! N.

The 'F - category of the pair (M;N) is de_ned by

'F(M;N) = minf_(f) : f 2 Fg

where _(f) is the size of the critical set C(f) of f . It is clear that 0 _ 'F(M;N) _

1 and we have 'F(M;N) = 0 if and only if family F contains immersions (if

m < n), submersions (if m > n) or di_eomorphisms (if m = n). In this presen-

tation, we shall point out some important particular situations for the family F .

Some su_cient conditions for 'F(M;N) = 1 are presented. Also, we give some

applications of the main results as well as some open problems.

Friday, October 16, 2009

Professor Mario Roy, York University, Canada

Behavior of the Pressure and Hausdorff Dimension in

Non-Irreducible Graph Directed Systems.

Abstract: The behavior of the pressure function associated with finitely

irreducible conformal graph directed Markov systems has

been described a decade ago by Mauldin and Urbanski.

They further showed that the Hausdorff dimension of the limit

sets of such systems may be obtained by a variation of the

famous Moran-Bowen formula. In this talk, we will discuss the

behavior of the pressure and the Hausdorff dimension in

non-irreducible systems

Friday, September 25, 2009

Dr. Karen Brucks from The University of Wisconsin.

Selected Jewels from One-Dimensional Dynamics

Abstract: We investigate asymptotic behaviors of one dimensional dynamical systems. Tools and jewels to be discussed include: Kneading Maps, Hofbauer Towers, Adding Machines, Strange Adding Machines, Inverse Limit Spaces, Phase Portraits, and the Farey Tree.

Friday, April 3, 2009

Steve Dilworth of University of South Carolina.

Convergence of some greedy algorithms in Banach spaces

Let D be a fundamental set in a a Banach space X. Greedy algorithms provide an intuitively appealing method for approximating a given vector by a linear combination of vectors in D. The convergence of these algorithms in Hilbert space is well understood. We consider some natural generalizations of the Hilbert space algorithms to the Banach space setting and examine their convergence properties with respect to either the norm or the weak topologies.

Friday, March 6, 2009

David Manderscheid, Dean, College of Arts and Sciences, University of Nebraska-Lincoln

Talk 1 of 2

Recruiting and Retaining PhD Students in the Mathematical Sciences.

Recruiting and Retaining PhD Students in the Mathematical Sciences In this interactive talk we will discuss proven methods to increase the number of PhDs in mathematics awarded to members of underrepresented groups. I will highlight examples from Arizona State University, the University of Iowa, and the University of Nebraska. We will also discuss the findings of the Carnegie Foundation for the Advancement for Teaching in their work with PhD programs in mathematics from across the US. Mentoring to create a community of scholars is key. Throughout an emphasis will be placed on methods that lead to better success for all students.

Talk 2 of 2

Langlands Functoriality and Howe Correspondences: An Introduction and Three Examples.

Abstract: Langlands Functoriality and Howe Correspondences: An Introduction and Three Examples Functoriality and theta (Howe) correspondences are the two most common ways to construct the representations that arise in the modern theory of automorphic forms. Comparing these methods can lead to striking examples with profound implications for number theory, e.g., counterexamples to the Generalized Ramanujan Conjecture. In this talk I will give an introduction to functoriality and theta-correspondences and then look at three examples of how the methods compare.

October 17, 2008

Ted Hill, Georgia Tech (www.math.gatech.edu/~hill)

Benford's Law in Dynamical Systems

The century-old empirical observation called Benford's Law (BL) states that the significant digits (mantissas) of many real datasets are logarithmically distributed (e.g., more than 30% of the leading decimal digits will be 1, and fewer than 5% will be 9), rather than uniformly distributed as might be expected. This talk will briefly review some of the basic probabilistic theory underlying BL, mention recent empirical evidence, and then focus on the surprising ubiquity of BL in classical deterministic sequences and dynamical systems. For example, it has long been known that the powers of 2, Fibonacci and Lucas numbers, and (n!) all follow BL. Recent developments show that iterations of large classes of common functions (including all polynomials, power, exponential, and trigonometric functions, and compositions thereof), geometric Brownian motion (hence many stock market models), and many classical ODE's and numerical algorithms such as Newton's method, all produce BL distributions.

Applications of these theoretical results to practical problems of fraud detection, analysis of round-off errors in scientific computations, and diagnostic tests for mathematical models will be mentioned, as well as several open problems in dynamical systems, probability, number theory, and differential equations. The talk will be aimed for the non-specialist _______________________________________________

Dr. Coke S. Reed, Interactic LLP.

Parallel Computation, the Data Vortex and Dynamical Systems.
Coke Reed is a mathematician who has made substantial contributions to the subject of dynamical systems. He received a PhD from the University of Texas and was Professor at Auburn University.

At Auburn he spent summers at IDA (Institute for Defense Analyses) at Princeton. Coke left Auburn to become the first non administrative researcher at MCC in Austin. He left MCC to become full-time at IDA. While at IDA he began to develop ideas on computer design and eventually left there to found Interactic, a very innovative company devoted to the development of parallel computation. He has since moved Interactic from Princeton to Austin. His work on parallel computation is based on his ideas from dynamical systems. His talk will start with an introduction to the problems of parallel computation, particularly the growing disparity between processing speed and communication time. It will end with a view of the near future in parallel computation. His talk will be of general interest.

May 2, 2008

Hiro Terao (Hokkaido University, Japan)

Free Multi Arrangements

Free arrangements of hyperplanes have been studied since early 80s. We, however, still don't know exactly what they are. A recent important work of M. Yoshinaga (Invent. Math. 2004) tells us that we have to know what free multi-arrangements are in order to know what free arrangements are. Although the study of free multi-arrangements is in its infancy and little is known, we now understand the freeness of multi-reflection (Coxeter) arrangements reasonably well. In this talk we summerize basic known results on free multi-arrangements which were obtained recently, including the multi addition-deletion theorem and the multi characteristic polynomials (both by Abe-Terao-Wakefield).

Apr 18, 2008

John Michael Neuberger (Northern Arizona University)

The Existence, Nodal Structure, and Approximation of Solutions to Nonlinear Elliptic Partial Differential and difference Equations (PDE and PdE).

Apr 11, 2008

Mike Keane (Wesleyan University)

The M/M/1 Queue is Bernoulli

Abstract: The classical output theorem for the M/M/1 queue, due to Burke (1956), states that the departure process from a stationary M/M/1 queue, in equilibrium, has the same law as the arrival process. That is, it is a Poisson process. I consider the dynamical system which arises from the transformation associating to each arrival process the corresponding departure process - by Burke's theorem, this yields, correctly viewed, a measure-preserving transformation. Our investigations show that a simplified version of this dynamical system, seen at so-called event times, is isomorphic to a Bernoulli scheme with a countable alphabet in a natural manner. Seen intuitively, if we regard an infinite sequence of M/M/1 queues chained together, the departure process of each of them being used as the arrival process of the next one, then the sequence of queue lengths at an event time are independent and identically distributed, and determine the sequences of queue lengths at any other event time. In this sense, although the system at event times is deterministic, there is a strong loss of information between queues which are far away from each other in the chain. The lecture supposes no previous knowledge of queueing theory or of ergodic theory. It concerns joint work with Neil O'Connell, currently at Warwick University.

April 2, 2008

Pandelis Dodos (Université Pierre et Marie Curie - Paris 6, France)

"Classes of Banach spaces admitting small universal spaces."

Let C be a class of Banach spaces. A Banach space Y is said to be a universal space for the class C if Y contains an isomorphic copy of every member of C. We shall present the solution to the following problem. (P) Let C be a class of separable Banach spaces. When can we nd a separable Banach space Y which is universal for the class C but not universal for all separable Banach spaces?

March 27, 2008

J.B. Nation (University of Hawaii)

Reflection Group Codes and their Decoding

In 1968, Slepian introduced group codes for the gaussian channel."

The idea was to choose a group of orthogonal matrices and a point on

a sphere in $R^n$, and then use the orbit of that point by that group

as a set of signals for communication. At the time, the method was not

practical, but in the interim computer speeds have increased dramatically

and the algorithm has been refined. We present a version that may be

competitive with other modulation schemes.

February 15, 2008

Jon Kujawa (University of Oklahoma)

Title: Calculating Cohomology using Invariant Theory

Starting with the 21st century question of calculating cohomology for Lie superalgebras, we quickly find ourselves using the 19th (and 20th) century tools of invariant theory. We will discuss Lie superalgebras and their cohomology and how invariant theory fits into the picture. For most of the talk we will focus on what happens in the specific case of the Lie superalgebra gl(m|n). The talk will start at the beginning and not assume a knowledge of Lie superalgebras, cohomology, or much other post WWII mathematics. It should be accessible to all.

Feb. 12t 2008

Zoltan Buczolich (Eotvos University, Hungary)

Title: Universally L1 good sequences with gaps tending to infinity

See pdf file: Buczolich Abstract

Feb. 8, 2008

Mark Levi (Penn State)

Physical reasoning in mathematics

Abstract: Some mathematical problems can be solved by a "physical/mechanical" argument, sometimes with surprising ease. I will describe a few of these problems, starting with the more basic (the Pythagorean theorem, the Pappus' area and volume theorems) and ending with the more advanced, e.g., the Riemann Mapping Theorem. In addition to the above, here are some other theorems made simple by physics: the Gauss-Bonnet theorem, Moser's theorem on uniformization of density, and the theorems of Green and Stokes. The derivation of the Euler-Lagrange equations from calculus of variations gains a surprisingly simple mechanical explanation, as does the preservation of Poincaré's integral invariants. I will discuss a selection from this list, subject to the constraint of time. The discussion will require no tools beyond calculus and will be self-sufficient in terms of mechanics required.

Nov. 16, 2007

Amy Glen (University of Quebec at Montreal, Canada)

Markoff's condition and Christoffel words

Abstract: In studying the minima of certain binary quadratic forms AX^2 +2BXY + CY^2, A. Markoff (1879, 1880) introduced a necessary condition that a bi-infinite word must satisfy in order that it represent the continued fraction expansions of the two roots of AX^2 +2BX + C. In this talk I will introduce "Markoff words" as certain factors appearing in bi-infinite words satsifying the "Markoff condition". I will show that these words coincide with the so-called "central words" appearing in "Christoffel words", which can be geometrically realized as discretizations of line segments in the plane by paths on the integer lattice.

N.B. This is joint work with Aaron Lauve and Franco Saliola.

November 9, 2007

Matt Papanikolas (Texas A&M University)

Survey of transcendental number theory

Abstract

November 2, 2007

Thomas Schlumprecht (Texas A&M University)

Small Subspaces of L_p

Abstract

October 5, 2007

Properties of Hausdorff dimension in families of conformal IFS

Abstract:

In this talk, I will successively discuss the continuity and real-analyticity

properties of the Hausdorff dimension function in finite and infinite

families of conformal iterated function systems.

April 20, 2007

Ralf Schmidt (University of Oklahoma)

Riemann's 1859 paper

Abstract: In 1859 Riemann's paper on what we now call the Riemann zeta function appeared. I will report on the main ideas appearing in this famous work. It is also the paper in which the Riemann hypothesis is first formulated.

March 30, 2007

Idris Assani (University of North Carolina at Chapel Hill)

On A. Zygmund's di®erentiation conjecture

Abstract

March 9, 2007

Pramod Achar (LSU in Baton Rouge)

Springer correspondences for dihedral groups
Let G be a reductive algebraic group, and let W be its Weyl group. (For example, if G = GL(n), then W is the symmetric group.) A recurring theme in representation theory is the fact that many deep ideas and sophisticated structures attached to G are accessible via fairly elementary calculations in terms of W. Weyl groups themselves are fairly well-understood---they are all crystallographic finite Coxeter groups, which have been studied since at least the 1930's -- so this means we can really "get our hands on" abstract things like perverse sheaves on the unipotent variety of G.

Now, suppose we start with a group W that's not a Weyl group of anything, but is close: perhaps a non-crystallographic Coxeter group, or even a complex reflection group. Many representation-theoretic calculations still make sense, and the results have some shocking properties (various compatibility, integrality, and positivity conditions that are all explained by G in the Weyl group case). It looks as though we're studying the representation theory and geometry of nonexistent'' algebraic groups! I will discuss various results in this vein, in particular for the case where W is a dihedral group. This is joint work with A.-M. Aubert.

Friday March 2, 2007

Tomi Karki (University of Turku, Finland)

Word combinatorics with similarity relations

Abstract: We consider words, i.e., strings over a finite alphabet together with a similarity relation induced by a compatibility relation on letters. This notion generalizes that of partial words. Especially, we study periodicity. We introduce three types of periods, namely global, external and local relational periods, and we compare their interaction properties by proving variants of the theorem of Fine and Wilf for these periods.

Friday, Feb. 9, 2007

Zoltán Buczolich (Eotvos University, Hungary)

Abstract

Feb. 7, 2007

Hiroki Sumi (University of Osaka, Japan)

Title: The space of postcritically bounded 2-generator polynomial semigroups with hyperbolicity

Abstract:

Nov. 17, 2006

George Androulakis (University of South Carolina)

The Ramsey result of Gowers on partitions of block sequences of a Banach space.

Abstract: The classical Ramsey theorem refers to partitions of the set of all subsets of the integers with two elements. The corresponding Ramsey result for partitions of all finite normalized block sequences of a Banach space was proved by T.W. Gowers in 2002 and has a game theoretical formulation. The original proof was very involved. I will present an easy to understand proof of this result. This Ramsey result is very important because it yields the well known Gowers' dichotomy which was used to solve the famous homogeneous Banach space problem of S. Banach. This is a joint work with S. Dilworth and N. Kalton.

Oct 27, 2006

Kathrin Bringmann (Univ. of Wisconsin and Univ. of Minnesota)

Freeman Dyson's "Challenge for the Future": The mock theta functions.

In his last letter to Hardy, Ramanujan defined 17 peculiar functions which are now referred to as his mock theta functions. Although these mysterious functions have been investigated by many mathematicians over the years, many of their most basic properties remain unknown. This inspired Freeman Dyson to proclaim

"The mock theta-functions give us tantalizing hints of a grand synthesis still to be discovered. Somehow it should be possible to build them into a coherent group-theoretical structure, analogous to the structure of modular forms which Hecke built around the old theta-functions of Jacobi. This remains a challenge for the future."

Freeman Dyson

1987, Ramanujan Centenary Conference

Here we announce a solution to Dyson's "challenge for the future" by providing the "coherent group-theoretical structure" that Dyson desired in his plenary address at the 1987 Ramanujan Centenary Conference.

In joint work with Ken Ono, we show that Ramanujan's mock theta functions, as well a natural generalized infinite class of mock theta functions may be completed to obtain Maass forms, a special class of modular forms. We then use these results to prove theorems about Dyson's partition ranks.

In particular, we shall prove the 1966 Andrews-Dragonette Conjecture, whose history dates to Ramanujan's last letter to Hardy, and we shall also prove that Dyson's ranks explain' Ramanujan's partition congruences in an unexpected way.

September 22, 2006

Anne Zdunik (University of Warsaw)

Dynamics of meromorphic maps; measures and dimensions.

Abstract: In last years there have been a growing interest in the dynamics of meromorphic maps in the complex plane. We shall discuss various geometric (dimensions) and dynamical aspects of the structure of invariant sets and invariant measures for a large class of entire and meromorphic mappings. Some natural open questions will be also presented.

Thursday, July 20th

Ty Thompson-CO School of Mines

Solution Estimates for the Ginzburg-Landau Superconductivity Model on Thin Disks

April 21, 2006

Symmetry and Supersymmetry

Abstract: Supersymmetry is a discovery of the physicists in the 1970's which extends the classical notion of symmetry to the world of elementary particles and their fields. Its origins lie in the dichotomy of this world of particles into bosons and fermions. Supersymmetries are transformations between these two kinds of particles. Physicists believe that any theory unifying all the fundamental forces will be supersymmetric. Mathematically, supersymmetry involves a generalization of geometry in which the local coordinates include the usual commuting coordinates and additional anticommuting coordinates. The automorphisms of such supermanifolds are supersymmetries. In this talk I shall present an elementary account of the basic concepts and attempt to link the mathematics with physics. Very little technical background is needed for understanding the talk.

April 14, 2006

Professor Steven Hurder, University of Illinois at Chicago

Title: Foliations - a playground for topology and dynamics

Abstract: A foliation is a way to partition a manifold into a regular system of smaller components, the leaves, which are immersed submanifolds. A decomposition into 1-dimensional submanifolds is just a traditional dynamical system, while a partition into submanifolds of dimension larger than one incorporates many ideas from traditional topology, and yet is often an invitation to chaos. The motivation for the study of foliations is that they arise in many different settings, as they are used to solve problems in geometry, dynamical systems, analysis and even physics. One of the beauties of their study is that to understand them often requires equal measures of ideas from geometry, topology, and dynamical systems, and the most interesting and often difficult questions ask how these aspects play together. This talk will give an introduction to the topic, and present some recent results about the dynamics and topology of foliations.

April 7, 2006

Hales (CCR in La Jolla)

Title: Jordan Decomposition in Integral Group Rings

Abstract: Let A be a square matrix with rational entries. Then A can be written as the sum S + N where S and N also have rational entries, S is semisimple, N is nilpotent, and S and N commute. This representation is unique, and is called the Jordan decomposition of A. It can be considered as a coordinate-free, and ambient-field-free, version of the usual Jordan canonical form for matrices. This decomposition (in its multiplicative version) is particularly useful in the study of algebraic groups. If G is a finite group and u is an element of the rational group ring Q[G], i.e. u is a linear combination of group elements with rational coefficients, then there is an analogous decomposition: u = s + n where s and n lie in Q[G], s is semisimple, n is nilpotent, and s and n commute (this representation is also unique). Consider the integral versions of these decompositions: if the matrix A has integer entries, need S and N have integer entries? if the element u in Q[G] has integer coefficients, need s and n have integer coefficients? We give complete answers to these questions. The multiplicative version of the integral group ring question is much more subtle, however - for this we give a complete answer when G has 2-power order, and partial results in the general case.

March 31, 2006

Nat Thiem (Stanford University)

Title: Hecke algebras in combinatorial representation theory

Abstract: Hecke algebras appear as valuable tools in many areas of mathematics including algebra, geometry, number theory, and physics. This talk explores how Hecke algebras can interpolate between the representation theory of groups of Lie type (such as the general linear group over a finite field) and the natural combinatorics associated with finite reflection groups (such as the symmetric group). After reviewing some of the fundamental questions in combinatorial representation theory, we will explore various definitions of Hecke algebras, describing how they feel" like reflection groups but see" representations of larger groups. While many of the results and techniques are more general, this talk will largely focus on the fundamental example involving the symmetric group and the the general linear group.March 24, 2006

Ben Miller (UCLA)

Coordinatewise decomposition of Borel functions

Abstract: We will discuss a variety of descriptive set-theoretic questions that have strong connections to their ergodic-theoretic counterparts. Our main focus will be on the following sort of question: Suppose that $S \subseteq \mathbf{R} \times \mathbf{R}$ is a Borel subset of the plane and $f : S \rightarrow \mathbf{R}$ is a Borel function. Under what circumstances are there Borel functions $u,v : \R \rightarrow \R$ such that $f(x,y) = u(x) + v(y)$?

February 24, 2006

Coefficient dynamics

Mike Keane (Wesleyan University)

Abstract: In this lecture, I describe an old method in a new setting which may be useful for the study of symbolic sequences obtained by expanding numbers either in continued fractions or in bases. After an introduction to the method, I intend to sketch an earlier result of mine which describes a possible way in which Gauss discovered the statistical distribution of partial quotients of continued fractions, some two hundred years ago. Then, using these ideas, I present what seems to be a new proof of an old theorem of Lagrange, stating that quadratic algebraic numbers have eventually periodic continued fraction expansions. Finally, I would like to discuss the conjecture that there are no irrational algebraic numbers belonging to the classical Cantor set, and present a new conjecture using dynamics which, if true, would lead to a partial solution of this problem.

Feb. 17, 2006

HongYang Chao (Sun Yat-Sun University, China).

Abstract: Iimage enhancement technology is always a hot topic in the area of digital image processing. This talk is mainly about improved histogram equalization. We will introduce a new method and will show how to improve the outlooking of image data from a digital camera, i.e. CCD data analysis. In addition, we will talk about why we have to do video compression and how people do it. Including some recent developments.

February 10, 2006

Peter Massopust, (Tuboscope Pipeline Services, Houston)

Data and Image Analysis in Pipeline Inspection

Abstract: One of the main tasks of the pipeline integrity industry is the detection and classification of defects in pipelines. There is a wide variety of defects but they can be put into essentially three major groups: (i) defects due to corrosion, (ii) defects generated by mechanical damage, and (iii) cracks created by stresses in the pipe wall. A general defect may belong to more than one group.

The main mathematical problems encountered when analyzing, enhancing, and evaluating data and images collected by inspection tools yield a plethora of beautiful and interesting mathematics ranging from partial differential

equations and special functions to wavelet, curvelets, and splines. In this talk, we will highlight some of these problems and their solutions and point out communalities with other data and image types such as biomedical measurements.

Jan. 20th, 2006

Edward Odell, (UT Austin)

Ramsey theory and Banach spaces

Abstract: Ramsey theorems have a certain general flavor. A structure is (usually) finitely colored. A certain monochromatic substructure of a certain type and size is sought. This is then shown to hold true if the original structure is sufficiently large, sometimes with added restrictions as to the nature of the coloring. In this expository talk we will discuss some Ramsey theorems and their impact on problems in the geometry of Banach spaces and vice versa.

Ramsey theory and Banach spaces

Fall 2004 - Fall 2005

Tuesday, Dec. 6th, 2005

Tony Zettl (Northern Illinois University)

Eigenvalues of Sturm-Liouville Problems

Abstract: We discuss eigenvalues and eigenfunctions of classical regular self-adjoint Sturm-Liouville problems. Then indicate extensions to some nonclassical cases: non-self-adjoint, indefinite, singular.

December 2, 2005

Walter Bergweiller (University of Kiel, Germany)

Fixed points and periodic points of quasiregular maps

Let f,g be a quasiregular self-maps of d-dimensional Euclidean spacewith an essential singularity at infinity, where d>1. We will discuss two results concerning such mappings. The first result, due to Heike Siebert, says that if n>1, then f has infinitely many periodic points of period n. This means that the n-th iterate has infinitely many fixed points that are not fixed points of any k-th iterate where k<n. The second result says that the composite function f(g) has infinitely many fixed points. The proofs are based on normal family arguments, and thus we shall also discuss normal family analogues of the above results. The results above where known before if d=2 and the functions f,g are holomorphic (and they had been conjectured by Baker and Gross for this case). The present approach leads to new and simpler proofs for this special case.November 4, 2005

Voker Mayer (University of Lille, France)

Thermodynamical formalism for meromorphic functions of finite order

We present joint work with Mariusz Urbanski in which we make available, for a wide class of meromorphic functions, one of the main tools for the geometric study of the Julia set. Namely, based on Nevanlinna theory, we proof that the thermodynamical formalism is valid for very general hyperbolic meromorphic functions of finite order (including exponential, sine and tangent families). Then we give geometric applications such as Bowen's formula: the Hausdorff dimension of the radial Julia set is given by the (only) zero of the topological pressure. The Question of Concreteness of Cofinitary Subgroups of the Infinite Symmetric Group.

October 21, 2005

Kathrin Bringmann (University of Wisconsin at Madison)

On Mock Theta functions and a Conjecture of Dragonette and Andrews.

This is a joint work with Ken Ono.

We solve the classical problem of obtaining formulas for $N_e(n)$ (resp. $N_o(n)$), the number of partitions of an integer $n$ with even (resp. odd) rank. Thanks to Rademacher's exact formula for the partition function, this problem is equivalent to that of obtaining a formula for the coefficients of the mock theta function $f(q)$, a problem with its own long history dating to Ramanujan's last letter to Hardy. Little was known about this problem until Dragonette in 1952 obtained asymptotic formulas. In 1966, G. E. Andrews refined Dragonette's results, and conjectured an exact formula for the coefficients of $f(q)$. By constructing a weak Maass-Poincare series whose holomorphic part" is $q^{-1}f(q^{24})$, we prove the Andrews-Dragonette conjecture, and as a consequence obtain the desired formulas for $N_e(n)$ and $N_o(n)$.

September 16th, 2005

Bart Kastermans (University of Michigan)

The Question of Concreteness of Cofinitary Subgroups of the Infinite Symmetric Group.

A question often encountered in mathematics is how concrete certain types of objects can be. This is a question with immediate intuitive meaning, but with just this intuitive meaning not subject to study (certainly not in case of a negative answer). In this talk I will explain how it translates to a precisely stated logical question.

The second component of this talk is about maximal cofinitary groups. These are certain subgroups of the infinite symmetric group. The difficulties in constructing these groups are often of a combinatorial nature.

In this talk I will introduce maximal cofinitary groups. Then give some of their basic properties, and show how these lead to interesting questions. I will explain the question of concrete such groups, how to study it, and give the results so far known. Then I'll show some of the ingredients in constructing them, and end with some open questions.

September 9, 2005

Hiroki Sumi (Osaka University, Japan)

Random dynamics of polynomials and devil's-staircase-like functions in the complex plane

We consider random dynamics of polynomials on the complex plane. More precisely, let $tau$ be a Borel probability measure in the space of polynomials and we consider i.i.d. random dynamical systems on the Riemann sphere such that at every step we choose a polynomial according to the distribution $/tau .$ Let $T(z)$ be the probability of tending to infinity from the initial value $z.$ Suppose that the support of $tau$ is compact, the postcritical set of semigroup $G$ generated by the support of $tau$ is bounded in the complex plane, and the Julia set of $G$ is disconnected. Then we show that the function $T$ on the Riemann sphere has the following properties. (1) $T$ is continuous on the Riemann sphere. (2) $T$ on the Riemann sphere has the following properties. (1) $T$ is continuous on the Riemann sphere. (2) $T$ varies only on the Julia set of $G$. (3) $T$ has some monotonicity property. Hence $T$ is like the devil's staircase.

May 5, 2005

Genevieve Walsh, UT Austin

"Which 3-manifold is the universe?"

The surface of the earth is a 2-manifold, which means that it is locally modelled on $R^2$. In fact, we know exactly what 2-manifold it is, the 2-sphere. Similarly, our universe is a 3-manifold, meaning locally modelled on $R^3$. In this talk, we will explore the various possibilities for the 3-manifold that is our universe.

April 29, 2005

Charles Holton, UT Austin

"The C*-algebraic Rohlin property for shifts of finite type"

The Rohlin property for an automorphism of a C*-algebra can be thought of as a noncommutative topological analogue to the Rohklin Lemma of ergodic theory. We briefly describe a construction of a C*-algebra and an automorphism from a shift of finite type. We then expound at great length on the definition and significance of the Rohlin property, and how one can deduce it from an "approximate" Rohlin property. The main result is that the Rohlin property holds for an automorphism constructed from a shift of finite type, and hence the C*-crossed produce of the algebra and the automorphism is determined up to automorphism by K-theoretic data.

April 1, 2005

Julie Hartmann, University of Heidelberg

"Galois Groups of Linear Differential Equations"

Galois theory is the study of polynomial equations and their solvability by means of their symmetry groups, the so-called Galois groups. This theory was generalized by Picard, Vessiot and later Kolchin to linear differential equations. The differential Galois groups are matrix groups (more precisely, linear algebraic groups) acting on the solution space. The talk will give an introduction to the subject and report on recent developments, with particular focus on the inverse problem, i.e., the question which matrix groups occur as symmetry groups of linear differential equations. The main result we present is that over a rational function field with algebraically closed field of constants of characteristic zero, every linear algebraic group occurs as the Galois group of a linear differential equation.

April 7, 2005

Henk Bruin, University of Surrey

"Renormalization for piecewise rotations on the circle"

Interval translation maps (which generalize interval exchange transformations) can have interesting Cantor attractors. In this joint work with Serge Troubetzkoy (Luminy), we studied the occurrence and geometry of such attractors for maps of the circle consisting of two rotations. The main tool is a renormalization operator which acts on the parameter space as an infinite alphabet Horseshoe map with a neutral fixed point. A symbolic coding of the parameter determines the Hausdorff dimension and (non)unique ergodicity of the attractor.

March 28, 2005

Ioana Ghenciu, University of Wisconsin, River Falls

"Complemented Spaces of Operators, Dunford-Pettis and Gelfand-Phillips Properties"

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March 21, 2005

Ozlem Imamoglu, ETH Zurich

"Representation of integers as sums of squares, old and new results"

The problem of finding explicit formulas for the number or representations of an integer as a sum of squares has a long history. After briefly introducing the problem and its history, I will report on some recent results.

December 14, 2004

Dr. Hiroaki Terao, Tokyo Metropolitan University

December 10th

Dr. Giorgio Fusco, Università di L'Aquila, Italy

"Numerical Experiments and Conjectures on the Dynamics defined by some Singularly Perturbed Non-Convex Functionals of the Gradient."

We consider a class of non-convex functional in one space dimension. The gradient flow associated to such functional is ill posed. Therefore we regularize by perturbing with a small higher order term. We discuss various nonlinear phenomena of the regularized dynamics for small value of the perturbative parameter. In particular we describe three well separated time scales and formation and evolution of interfacies. We also discuss the possibilty of defining a notion of weak solution for the original unperturbed ill posed problem. Our approach is both theoretical and numerical.

October 15, 2004

Dr. Eugen Mihailescu, Institute of Mathematics of the Romanian Academy

"Thermodynamic formalism and higher dimensional complex dynamics"

In this talk we will review some of the most important features of dynamics in several complex variables. This can be done for automorphisms in C^n or for endomorphisms in P^n. We will focus mainly on the case of holomorphic endomorphisms and give some constructions, methods and results. Thermodynamic formalism is used in this setting to estimate the Hausdorff dimension of certain fractal sets. A new notion of inverse pressure will be introduced in the general continuous case (no holomorphicity required) and will be applied to dimension estimates.

October 8, 2004

Dr. Ted Slaman, UC Berkeley

"Measures and Their Random Reals"

I will begin with an overview of the effective randomness of an infinite sequence, including a discussion of the equivalent characterizations by Martin-L\"of in terms of measure and by Kolmogorov in terms of descriptive complexity. Then, I will discuss joint work with Jan Reimann, University of Heidelberg, in which we examine reals which are random for measures other than the standard Lebesgue measure. As an example, I will go into some detail about the following theorem.

Theorem (joint with Reimann) For $X\in 2^{\omega}$, the following conditions are equivalent.

1. There is a probability measure $\mu$ on $2^\omega$ such that $X$ is not a $\mu$-atom and $X$ is random relative to $\mu$.

2. $X$ is not recursive.

Fall 2003 - Spring 2004
April 30, 2004

Dr. Debastien Ferenczi, IML-CNRS, Marseille, France

"Substitutions on an Infinite Alphabet"

Abstract: A substitution on an alphabet A is an application from A to the set of finite words on A; under mild conditions, it has an infinite sequence as a fixed point, and the shift on its closed orbit gives a substitution dynamical system. When A is finite, these are compact topological dynamical systems, which are generally minimal and uniquely ergodic, and finite rank measure-theoretic dynamical systems. We study here a few examples where A is infinite: the infini-Bonacci system, which keeps most properties of the finite case; cases where the matrix is positive recurrent, where we have still a finite measure-preserving ergodic system; and the drunkard substitution, where we get an infinite measure- reserving system for which we can prove ergodicity. Though the rank is not finite, Rokhlin stacks are still the main tools of our study.

April 23, 2004

Dr. Ron Solomon, Ohio State University

"Finite Simple Groups from Galois to Aschbacker"

The concept "groupe simple" was introduced by Galois in 1832. A concerted effort to classify all finite simple groups was proposed by Holder in 1892, but it did not really take flight until the 1950's. The project seems at last to have been completed by Aschbacher and Smith this year. Along the way, many insights were gained about the structure of finite groups, and several amazing new mathematical objects were discovered. Many questions have been answered, but several mysteries remain. This talk will touch on some of the highlights and mention some open questions.

April 2, 2004

Dr. Allen Butler, Wagner Associates

"The Mathematics of Data Fusion"

In recent years, tremendous strides have been made in the improvement of existing and the development of new, more powerful, sensor systems. The result is a tidal wave of data which threatens to overwhelm the user, rather than assist her. The process of automatically filtering, aggregating and extracting the desired information from multiple sensors and sources is an emerging technology, commonly referred to as Data Fusion. In this talk, I will show how a wide variety of mathematical techniques are applied in this new discipline. I will begin with a discussion of the state estimation problem determining the current position and velocity of an object based on a set of discrete observations (e.g. radar tracking of an aircraft). I will discuss a number of filtering techniques, including the a-b filter, the classic Kalman Filter, the Extended Kalman Filter and the Unscented Kalman Filter. I will then discuss the data association problem given a set of observations or measurements taken over a period of time, determine which ones originate from the same real-world object. I will consider both real-time solution techniques and batch techniques such as those based on the Expectation-Minimization algorithm. Finally, I will conclude with a discussion of Data Fusion Measures of Performance, attempting to answer the question, How do you grade a system that produces probability distributions for answers?

March 9, 2004

Dr. Ralph Chill, Ulm University

"Around the Lojasiewicz-Simon inequality and its applications to PDEs"

The talk will start with an easy proof that bounded and global solutions of finite-dimensional gradient systems converge to a steady state if the underlying energy satisfies the Lojasiewicz inequality. It turns out that the same proof works for the semilinear heat equation or the semilinear wave equation. Motivated by this, we study theoretical aspects of the Lojasiewicz inequality (gradient inequalities), its generalization to infinite dimensions, we show how to recover known convergence results and we indicate how to prove similar results for a variety of PDEs and for the steepest descent method.

March 5, 2004

Xinfu Chen, University of Pittsburgh

"Interfacial Dynamics and Free Boundary Poblems"

Interfacial phenomena are commonplace in physics, chemistry, and in various other fields. They occur whenever a medium is present that can exist in at least two different states and there is some mechanism that generates or enforces a spatial separation between these two states. The separation boundaries are then called interfaces of free boundaries. Generally speaking, the study of interfacial phenomena can be grouped into two categories:

(i) free boundary models in which states (phases) are described by binary valued phase indicator functions and free boundaries are hypersurfaces where the phase indicators switch their values.

(ii) continuum models in which states are described by smooth functions which experience large gradients in places called interfacial regions.

In the ideal limit of a continuum model, a smooth phase indicator function becomes binary valued, the thickness of an interfacial region becomes zero, and the interfacial region becomes a free boundary. In this talk, a few examples will be given to illustrate both models and their relationships.

February 13, 2004

Zoltan Buczolich, Department of Analysis, Eotvos Lorand University, Budapest, Hungary.

"An L1 Counting Problem in Ergodic Theroy"

January 30, 2004

Paula Cohen, Texas A&M University

"Hyperbolic Distribution Problems"

Siegel in 1932 and Schneider in 1937 obtained the first results on the transcendence and linear independence of periods of classical doubly periodic functions. This led to the first results on the transcendence at algebraic points of 1-variable complex functions invariant with respect to discrete groups of fractional linear transformations (modular groups). We discuss some problems that arise in the modern outgrowth of this work. These problems motivate the study of distribution problems for certain families of points on modular varieties, in particular questions of equidistribution. The talk will be accessible to the general audience.

September 19, 2003

Christian Wolf, Wichita State University

"Measures of maximal dimension for hyperbolic diffeomorphisms"

We discuss the existence of ergodic measures of maximal Hausdorff dimension for hyperbolic sets of surface diffeomorphisms. This is a dimension- heoretical version of the existence of ergodic measures of maximal entropy. The crucial difference is that while the entropy map is upper-semicontinuous, the map $\nu\mapsto\dim_H\nu$ is neither upper-semicontinuous nor lower-semi\-continuous. This forces us to develop a new approach, which is based on the thermodynamic formalism. Remarkably, for a generic diffeomorphism with a hyperbolic set, there exists an ergodic measure of maximal Hausdorff dimension in a particular two-parameter family of equilibrium measures.

October 23, 2003

Benedikt Lowe, University of Amsterdam

"Blindfolding stochastic opponents in infinite games; or: How do you win infinite stochastic games if you can only train against dummies?"

Take a set A of infinite strings of zeros and ones and play the following infinite game: infinitely often, players I and II play single 0-1 bits and thus produce an infinite string of zeros and ones. We say that player I wins if this string lies in A, otherwise player II wins.

A winning strategy in such a game is a procedure to choose the next move that guarantees a win for the player using it against all counterstrategies. Peculiarly, in order to test whether a given strategy is winning, you only need to test it against fixed strategies, i.e., counterstrategies that don't react to your moves.

This property is lost if you move from strict winning strategies in the above sense to strategies that win with probability one. In this case, you could have a strategy that guarantees a win with probability one against all passive opponents, but loses with probability one against some active opponents. In this talk, we shall discuss consequences of this and means of dealing with it.

November 14, 2003

Brian Conrey (American Institute of Mathematics)

Title: "Random matrix theory and the Riemann zeta-function"

In 1972 a chance meeting between Hugh Montgomery and Freeman Dyson first led people to suspect that there was a relationship between the statistics of the zeros of the Riemann zeta-function and eigenvalues of random matrices. This relationship was developed over the years, notably through data found by Andrew Odlyzko. In 1998 a deeper connection was discovered between the value distribution of the zeta-function and the distribution of values of characteristic polynomials of these random matrices. Today we have an amazing set of parallels between the Riemann zeta-function (also families of L-functions) and unitary matrices (also orthogonal and symplectic matrices). In this talk we will describe some of these connections. We will focus especially on the random matrix side of this duality, and discuss some of the (elementary) techniques that prove the elegant theorems on this side. The talk will be aimed at a general audience.

November 21, 2003

Ion Mihai, University of Bucharest, Romania

"Kaehler Manifolds and Their Submanifolds"

The most important class of complex manifolds are the Kaehler manifolds. They are manifolds endowed with a special type of metric, the Kaehler metric. The complex n-space C^n (with the Euclidean metric), the complex torus T^n (with metric induced by the Euclidean metric on C^n), the complex projective space (with the Fubini- Study metric), the complex Grassmannian, the unit complex disk (with the Bergmann metric) are all examples of Kaehler manifolds.

However, there are interesting almost Hermitian manifolds which do not admit Kaehler metrics. It is known that the 6-dimensional sphere S^6 carries a distinguished non- aehler nearly Kaehler structure. There are cohomological obstructions to the existence of Kaehler metrics on compact complex manifolds. For instance, it can be shown that the Calabi-Eckmann manifolds (in particular, the Hopf manifolds) cannot admit any Kaehler metric.

Special classes of submanifolds of a Kaehler manifold can be defined according to the behavior of their tangent spaces under the action of the complex structure of the ambient space. We mention here: complex submanifolds, totally real submanifolds, slant submanifolds, CR-submanifolds.

In this expository talk we will introduce and comment on some of the objects named above.

December 9, 2003

Title: "On how potential theory sometimes pays back complex analysis"

Abstract: We will discuss two instances in which potential theory repays its debt to complex analysis in the form of applications to the theory of dynamical systems. We will first glance over some properties of the Julia set of rational functions, and then establish parallels for the attractor of iterated function systems. All pertinent notions will be introduced and exemplified during the talk.

Fall 2002 - Spring 2003
November 15, 2002

Anthony Quas, University of Memphis

Title: "Arrow's Impossibility Theorem"

Abstract: Arrow's Impossibility Theorem states that in an election with 3 or more candidates, there is no voting satisfying a small number of basic fairness requirements. In spite of this, many voting systems are used with a wide variety of properties. Here, we focus on the requirement of monotonicity: that the more votes you get, the more likely you are to win. Surprisingly, a fairly popular voting system does not have this property. We will discuss the probability that unfairness of this type arises in the single transferable vote system.

December 9, 2002

Sergey Yuzvinsky, University of Oregon

Title: "Topological robotics on hyperplane complements"

Abstract: We will start by defining a new simple invariant of topological spaces - topological complexity (TC). If one views a space X as the configuration space of a robot, then TC(X) describes roughly the complexity of a motion planning algorithm for the robot. We'll discuss the property of the invariant, and in particular, a lower bound for it coming from the ring theory. In the case when X is the complement of a complex hyperplane arrangement, the ring in question is defined by the underlying matroid---it is the Orlik-Solomon algebra of the matroid. Thus the problem of computing TC(X) includes the problem of computing a matroid invariant. We'll compute this invariant for the braid arrangements where TC(X) has a special importance because a motion on X is just a collision free motion of several ordered points on a plane. We'll also show the values of TC(X) for the configuration spaces of several distinct ordered points in the higher dimensional real spaces. At the end some problems and conjectures will be formulated.

January 24, 2003

Volker Mayer, Lille University, France

Title: "Renormalizations and Rigidity in Conformal Dynamics"

Abstract: We explain how renormalization techniques can be used to obtain simple proofs of rigidity phenomenas in holomorphic and quasiregular dynamics.

February 28, 2003

Thomas Schlumprecht, Texas A&M University

Title: "Can all the central sections of a bigger body be smaller?"

Abstract: We present a unified analytic solution to the following problem stated by Busemann and Petty (1956): Let K and L be two convex and symmetric n-dimensional bodies and assume that all the (n-1)-dimensional central sections of K have smaller volume than the corresponding sections of L. Does it follow that the volume of K is smaller than the volume of L?

March 6, 2003

Title: "An introduction to uniform distribution modulo 1"

Abstract: The aim of this talk is to give an introduction to the theory of uniform distribution modulo one. We will focus on the notion of discrepancy, that is on the quantitative aspect of this theory. We will deal in particular with questions related to number theory and diophantine approximation.

March 13, 2003

Marco Fontelos, Universidad Rey Juan Carlos, Spain

Title: "Singularities in fluids"

Abstract: In 1755 the Swiss mathematician Leonard Euler wrote for the first time the differential equations describing the motion of an inviscid (i.e. without internal friction forces) fluid. In 1822 C. Navier and, independently, G. Stokes introduced the viscosity term and obtained the so called Navier-Stokes system. Despite the apparent simplicity of the equations, most of the fundamental questions concerning them remain unsolved. It is not known, for instance, whether or not the solutions remain smooth for all time or form some kind of singularity. The later possibility could be related to the appearence of chaotic motions that are observed when the flow becomes turbulent.

In the talk we will present some results regarding the formation of singularities in fluids focusing on three situations: 1) the possible blow-up of the velocity field inside the fluid,
2) the existence of a topological transition in the interface between two fluids by which a simply connected fluid domain becomes disconnected (with the formation of drops),
3) the formation of wavy structures via Kelvin-Helmholtz instability. The appearance of these phenomena is very sensitive to the nature of the fluid. We will also briefly discuss the situation when the fluids presents some "elastic" behavior.

April 4, 2003

Mike Keane, Wesleyan University

Title: "On spontaneous emergence of opinions"

Abstract: One of the distinguishing properties of the present scientific method is reproducibility. In one of its guises, probability theory is based on statistical reproduction, near certainty being obtained of truth of statements by averaging over long term to remove randomness occurring in individual experiments. When one assumes, as is often the case, that events farther and farther in the past have less and less influence on the present, the probabilistic paradigm is currently well understood and is successful in many scientific and technological applications. Recently, however, we have come to realize that precisely in these applications important stochastic processes occur whose present outcomes are significantly influenced by events in the remote past. This behavior is not at all well understood and some of the simplest questions remain today irritatingly beyond reach. A salient example occurs in the theory of random walks, where there is a dichotomy between recurrent and transient behavior. After explaining this classical dichotomy, we present a very simple example with infinite memory which is neither known to be transient nor recurrent. Then, using a reinforcement mechanism due to POLYA, we explain the nature of a particular infinite memory process in terms of spontaneous emergence of opinions. Finally we would like to discuss briefly some of our recent results towards understanding the recurrence-transience dichotomy for reinforced random walks ,and indicate an application to universal coding used in optical CD technology.

April 11, 2003

Giorgio Fusco, University di L'Aquila, Italy

Title: "A regularized Perona-Malik functional: Some aspect of the gradient dynamics"

Abstract: We study an elliptic regularization of the classical Perona-Malik functional. After a suitable rescaling we characterize the Gamma-limit ot the regularized functional. We analize the gradient dynamic associated to the Gamma-limit and obtain some preliminary results concerning the convergence of the dynamic corresponding to the regularized functional to the one generated by the Gamma-limit.

April 25, 2003

AGANT Minhyong Kim, University of Arizona

Title: "The topology of algebraic surfaces and reduction modulo p"

Abstract: We will discuss some classical relationships between the mod p arithmetic of varieties and their topology. Furthermore, we will mention one new result regarding the homeomorphism type of simply-connected surfaces.

December 3, 2003
Title: "Porosities and dimensions"
Esa Jarvenpaa
Abstract: I will give a short survey on different notions of porosities and their relations to dimensions. Dimension is a concept which describes the size of a set or a measure. Porosity, in turn, tells how big holes there are in the set or measure. Intuitively, it seems natural that if there are a lot of big holes then the dimension cannot be very big. I will explain to which extend this intuitive picture is correct.

Fall 2001 - Spring 2002

G.A. Edgar, Ohio State University

Title: "How big is a subgroup of the reals?"

October 19, 2001

Abstract: Suppose a subset of the real line is "nice" both in a topological sense and in an algebraic sense. How big can it be? Topological versions of nice sets could be closed sets or especially Borel sets. Algebraic versions of nice sets could be subgroups, or subrings, or subfields. "how big" can be asked in several senses. One sense (Hausdorff dimension will be discussed, ranging from Volkman in 1960 up to current results.)

November 2, 2001

Vladimir Pestov, Victoria University of Wellington, New Zealand

Title: "Asymptotic geometric analysis and topological transformation groups"

Abstract: Asymptotic geometric analysis (also known as geometry of large dimensions) studies various counter-intuitive phenomena occuring in geometric structures of high finite dimension. The framework used is the concept of a metric space with measure (mm-space), and the theory is mainly concerned with the phenomenon of concentration of measure on high-dimensional structures. Among the best known manifestations of the phenomenon are the law of large numbers (probability), Dvoretzky theorem (geometric functional analysis), blowing-up lemma (coding theory), and many other results and techniques cutting across mathematical sciences. The present growth of interest in the subject is due to the work of Paul Levy, Vitali Milman, Michel Talagrand, Mikhail Gromov, and others. Many model examples upon which asymptotic geometric analysis is built are in fact transformation groups, and the concentration phenomenon in the phase space leads to dynamical phenomena, such as the existence of fixed points. Work by mathematicians including Milman, Gromov, Glasner, Furstenberg, Weiss, Giordano, and the present author has led to new insights into the dynamical properties of some important infinite-dimensional' groups and representations in infinite-dimensional Hilbert spaces. In this talk we will survey the basic concepts of asymptotic geometric analysis and its applications in the context of dynamics and representation theory.

December 14

Hiroshi Suzuki, The Ohio State University, and International Christian University

Title: "On Weakly Distance-Regular Digraphs Highly regular graphs and digraphs"

Abstract: This is an introduction to distance-transitive graphs, distance-regular graphs, distance-transitive digraphs, distance-regular digraphs, weakly distance-transitive digraphs and weakly distance-regular digraphs. The class of weakly distance-regular digraphs is the largest class among them. My talk includes, historical background, basic properties, examples, and recent results on weakly distance-regular digraphs.

January 22, 2002

Eric Sommers, University of Massachusetts at Amherst

Title: "Coherent Sheaves on the Nilpotent Cone"

Abstract: I will survey results concerning the Grothendieck group of equivariant coherent sheaves on the nilpotent cone of a simple Lie algebra. The Grothendieck group (after Bezrukavnikov's proof of a conjecture of Lusztig) has two natural bases. One is indexed by the dominant weights of the Lie algebra; the other (which is much more difficult to construct) is indexed by equivariant irreducible vector bundles on the nilpotent orbits of the Lie algebra. I will discuss some of the representation theory and geometry behind this work, as well as attempts to explicitly describe the bijection between the two bases.

March 13, 2002

Robbert Fokkink, TU Delft, Holland

Title: "On the problems of Dido and Borsuk"

Abstract: The isoperimetric inequality says that of all geometric figures, the disk has the largest area compared to its circumference. This inequality has been generalized in many directions, using techniques from all branches of mathematics. This talk focuses on one particular version, called the isodiametric inequality. It turns out that this inequality is related to Borsuk's conjecture from convex geometry.

March 28, 2002

Lisa Bloomer, Middle Tennessee State University

Title: "Random Probability Measures with given Mean and Variance"

Abstract: The question "is there a natural way to construct random probability measures?" has been addressed in several ways since Dubins and Freedman proposed the question in 1963. Recently, the question was modified by Hill and Monticino to be "is there a natural way to construct random probability measures while incorporating given information?" I will review the original algorithm described by Dubins and Freedman and the algorithm described by Hill and Monticino that allows the mean of the measure to be specified in advance. Then I will describe several methods of choosing random probability measures while specifying the mean and the variance.

Fall 2000 - Spring 2001
September 1, 2000

Jean-Paul Allouche, Paris: (CNRS, LRI, Orsay, France)

Title: "Non-integer bases, iteration of continuous functions, and an arithmetic fractal"

Abstract: In a recent paper appeared in American Mathematical Monthly, V. Komornik and P. Loreti study the real numbers q in (1,2) such that the number 1 has a unique expansion in base q. They prove in particular that there exists a smallest such number q, say t, and that the base-t expansion of 1 is essentially the Thue-Morse sequence. We prove how this result is a reformulation of a result by M. Cosnard and the author (1983) that was obtained in the framework of iterations of unimodal continuous functions. Furthermore we confirm a conjecture of Komornik and Loreti on the irrationality of t by proving that this number is actually transcendental (the proof is easy up to using a theorem of Mahler). We conclude by exhibiting an arithmetic fractal related to the above questions.

September 8, 2000

Hiroaki Terao (Tokyo Metropolitan University)

Title: "Double Coxeter arrangements, the Shi arrangements, anti-invariant
forms and logarithmic forms"

Abstract: Let W be a finite crystallographic group and A(W) be the arrangement of its reflecting hyperplanes in the n-dimensional real vector space. The Shi arrangement is A(W) together with the hypeperlanes defined by \alpha = 1 (\alpha is moving on the set of positive roots of W). It has remarkable combinatorial properties. For example, the number of chambers is equal to (1+h)^n (h is the Coxeter number). The "principal part" of the Shi arrangement is the double Coxeter arrangement. We prove that its derivation module is a free moduole of rank n with a basis consisting of derivations whose degrees are (h, h, ..., h). Explicit basis is described using the flat ructure (the Forbenius system) of Coxeter group. The relation between the anti-invariant differential forms and the logarithmic differential forms is also discussed.

September 25, 2000
Title: "A Progress Report on Jacobian Conjecture"
Daya-Nand Verma
Abstract: The said unsolved problem listed by Smale in his 1998 Math Intelligencer article as 16th of 18 Mathematical Problems for the 21-st Century amounts to asking for the Inverse Function Theorem of Algebraic Geometry,'' viz., to show that any polynomial endomorphism of the n-space (say over the complex numbers) with the Jacobian-determinant non-vanishing everywhere (IS INJECTIVE and hence) admits a polynomial inverse! It may not be too outrageous to say that the fact such a Statement is unproven (ever since its formulation for the case when n is 2 in 1939 by Ott-Heinrich Keller) is a dark spot' for 20th Century Algebraic Geometry, which was sometimes even taken as a matter of fact; lately the statement has even been subjected to doubts, and some exotic'' consequences of its falsity have been studied. After giving a quick survey of some of the relevant developments (mostly dating back to the 70's) I shall dwell a little on a recent new idea that could be called A Jacobian-Wronskian Approach to the Problem' <i.e. of the Proof of JC, for which I've now more faith in its truth>. A bit more precisely, I ask the NEW Question: How to give a GOOD Criterion to decide whether n given homogeneous polynomials in m variables, all of the same degree <or else, inhomogeneous polynomials in m-1variables>, are linearly independent?'' The meaning of good' should be guided by the answer classically available' when m is 2, in the form of (a slightly revised, homogenized, version of) the celebrated Wronski Theorem, basic to the Theory of Linear Ordinary Differential Equations. Thus one wants <a la Wronski'> the answer to be (almost) independent of the degree; however, for the actual application to the original Problem it's enough to consider m=n and d=3. Hence our more general enquiry may prove very valuable also to (an Algebrization Programme' for) the Theory of Linear Partial Differential Equation.

October 27, 2000

James T. Rogers, Tulane University

Title: "Boundaries of Siegel disks"

November 3, 2000
Title: "Random sets and the Loewner differential equation"
Steffen Rohde, University of Washington
Abstract: The Loewner differential equation, classically used by C. Loewner to study questions from geometric function theory, has recently been used by Lawler, Schramm and Werner to settle some outstanding problems in stochastics (such as the determination of the Hausdorff dimension of the Brownian frontier). In this talk I will explain the Loewner equation, its relation to stochastic growth models (such as loop erased random walk, percolation, Brownian motion) and will discuss some recent developments. The talk will be aimed at the non-specialist, and graduate students should be able to follow most of the talk.

November 13, 2000

Victor Nistor, Penn State University

Title: "Elliptic theory on singular and non-compact manifolds"

Abstract: The analysis on non-compact manifolds can sometimes be described by certain algebras of vector fields on suitable compactifications. To generalize the classical results on elliptic differential equations on compact manifolds to non-compact manifolds, Melrose has asked for algebras of pseudodifferential operators that quantize these vector fields and shown how to achieve this quantization in several particular cases, the best know being that of a manifold with cylindrical ends, which he compactified to a manifold with boundary, thus obtaining the so called "b-calculus." After reminding his results, as well as some related results of Mazzeo, I will explain how one can obtain a solution to Melrose's question in the spirit of Lie's third theorem (finite dimensional Lie algebras are integrable), using an idea of Connes. This then leads to the standard "elliptic package'' for operators in these algebras including criteria for compactness, boundedness, or Fredholmness. Using C^*-algebra methods, we also obtain the proof of another conjecture of Melrose on the spectrum of the Laplace operator.

January 26, 2001
Title: "On the wild components of the family $\lambda \tan(z)$"
Janina Kotus, Warsaw Instutute of Technology
Abstract: It is natural to ask if the hyperbolic components of the tangent family {\cal F}=\{\lambda \tan(z): \lambda \in \C-\{0\}\}$are the only open components of the$J$-stable maps. The evidence of the computer pictures indicates an affirmative answer to this so called {\it Densiy conjecture}. If the density conjecture is not true, there are non-trivial components of the$J$-stable set containing non-hyperbolic maps; we call them {\it wild components}. We prove that there are no wild components in the family$\cal F$for which the orbits of the asymptotic values are unbounded, what is a partial positive answer to the density conjecture. February 16, 2001 Title: "A Problem in Differential Equations with Disappearing Solution" Jim Serrin 1999-2000 September 14, 1999 Title: "Some aspects of the anticipating calculus for the Poisson process" Constantin Tudor, CIMAT and University of Bucharest Abstract: We use the Poisson-Ito chaos decomposition approach to define a variations derivative operator and its adjoint, which is an anticipating integrali.e., it agrees with the martingale Poisson-Ito integral for predictable integrands). Also an integration by parts formula and characterizations of these operators are given. October 7, 1999 Title: "Multifractal structure associated with Lyapunov exponents for dynamical systems" Yakov Pesin, Pennsylvania State University Abstract: Lyapunov exponents are fundamental invariants of dynamical systems that characterize stability of trajectories. They are often used in the numerical study of dynamical systems and are well related to other important invariants of dynamics such as entropy and fractal dimension. The behavior of the Lyapunov exponents on the base point is known to be extremely complicated and generates a highly non-trivial and remarkably refined multifractal structure which will be described in the talk. December 8, 1999 Title: "Unitary representations of Lie groups" Peter Trapa, Institute for Advanced Study, Princeton, NJ Abstract: Suppose$G_\R$is a real Lie group. A classical and still open problem is to describe all continuous, irreducible, length-preserving actions of$G_\R$on a Hilbert space. An impressive array of ideas has been applied to this problem with varying degrees of partial success. The purpose of this talk is to survey a handful of those ideas --- some algebraic, some geometric, and some arithmetic --- with a view toward optimistic applications of them. December 17, 1999 Title: "Projections of self-similar sets" Boris Solomyak, University of Washington Abstract: Replace the unit square by the union of four corner squares of side$1/4$. Iterating this construction yields a classical example of a self-similar set$K$in the plane, which has positive and finite one-dimensional Hausdorff measure, but is purely unrectifiable. It follows from Besicovitch's theory that$K$projects into sets of zero length on almost every line. I will present a self- contained proof of this fact, using just the Lebesgue density theorem. There are several related open problems which I am planning to discuss. (The talk is based on joint work with Yuval Peres and K\'{a}roly Simon.) January 28, 2000 Title: "Old and New Results on the Arc Structure of Singular Algebraic Varieties" Monique Lejeune-Jalabert, CNRS University Versailles St-Quentin Abstract: An arc on an algebraic variety$ V $defined over the complex numbers is a mapping from a sufficiently small neighborhood of the origin in the complex line into$ V $, given by convergent power series. By Artin's approximation theorem, for any nonnegative integer$ k $, the set of k-jets of arcs on$ V \$ is a constructible set (i.e. defined by polynomial equations and inequations). These constructible sets were first studied by J. Nash in connection with Hironaka's resolution of singularities. Further related developments will be reviewed.
This lecture is also sponsored by the Charn Uswachoke Lecture Series and the AGANT Lecture Series

March 6, 2000
Title: "From finite differences to finite elements--A short history of numerical PDE"
Vidar Thomee, Chalmers University of Technology, Sweden
Abstract: We describe the historical development of the basic approaches to the numerical solution of partial differential equations, namely finite difference and finite element methods. The properties of these classes of methods are compared for both stationary and evolution problems.

April 5, 2000
Title: "Complexity of Sequences and Dynamical Systems"
Sebastien Ferenczi, CNRS, Laboratoire de Mathematiques et Physique Theorique, Tours, France
Abstract: We study here the combinatorial notion of symbolic complexity: this is the function counting the number of factors of length n for a sequence, giving an indication of its degree of randomness. We give a survey of an open question which is still very much in progress, namely: to determine which functions can be the symbolic complexity function of a sequence. Then, we investigate the links between the complexity of a sequence and its associated dynamical system, and insist on the cases where the knowledge of the complexity function allows us to know either the sequence, or at least the system. This leads to another vast open question, the S-adic conjecture, and to a conceptual (though still conjectural) link with the notion of Kolmogorov-Chaitin complexity for infinite sequences. Also, these links with dynamical systems have been of considerable help to ergodic theory,and this prompted the ergodicians to create their own notions of complexity, mimicking the theory of symbolic complexity.

April 17, 2000
Title: "On Ostrowski's numeration system"
Valerie Berthe, CNRS Institut de Mathematique de Luminy
Abstract: The numeration scale of the Ostrowski numeration system is given by the denominators of the convergents in the continued fraction expansion of a given irrational number x. This system is particularly suited to study discrepancy properties of the sequence (nx). Our aim here is to explore the applications of this system to combinatorics on words. In particular, Ostrowski's numeration system is a very efficient tool for describing many arithmetic, ergodic and combinatorial properties of sequences obtained as codings of irrational rotations, the so-called Sturmian sequences. More generally, we will evoke the generalizations of these properties to two- dimensional sequences, three-interval exchange transformations and sequences with sub-affine complexity.

May 1
Title: "A short history of matroid representation theory"
Geoff Whittle, Victoria University, Wellington, New Zealand
Abstract: Matroids were introduced by Whitney in 1935 to axiomatise the combinatorial properties of a finite set of vectors in a vector space over a field. A matroid is representable over a field F if it is isomorphic to one that can be obtained from some set of vectors over F. A fundamental problem, mentioned by Whitney, is to decide which matroids are representable over which fields. This problem has turned out to be deep and has attracted some of the best researchers in combinatorics, eg Tutte and Seymour. Progress has been intermittent, but punctuated by some impressive and exciting results. The talk will survey the major results in the area. It is the speaker's intention and earnest hope that the talk will be accessible to a very general audience.

May 3
Title: "Forbidden Words in Symbolic Dynamics"
Filippo Mignosi, Universita di Palermo, Brandeis University
Abstract: We introduce an equivalence relation R on the set of functions from
to N where N denotes the set of natural numbers. By describing a symbolic dynamical system in terms of forbidden words, we prove that the R-equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that this new invariant is independent from previous ones, but it is not characteristic. In the case of sofic systems we prove that the R-equivalence of the corresponding functions is a decidable question. As a special application, we use this invariant to show that two systems associated to Sturmian words having `different slope'' are not conjugate. We also exhibit some connections between this invariant and a new data compression scheme.

May 24
Title: "Binary Self-dual Codes and Orthogonal Groups"
Akihiro Munemasa, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada and Graduate School of Mathematics, Kyushu University, Gakuoka, Japan
Abstract: Tonchev (1989), harada and Kimura (1995) gave a method to construct new doubly-even self-dual binary codes from a given one. Based on a joint work with Masaaki Harada and Masaaki Kitazume, we give an interpretation of their method in terms of transvections in an apprpriate orthogonal group, and describe a generalization of this method which leads to the enumeration of all doubly-even self-dual binary codes. We then discuss an analogue of doubly-even self-dual codes in arbitraty finite field of characteristic two. This new class of codes is also characterized as maximal totally singular subspaces with respect to a quadratic form.

1998-99
September 16, 1998
Title: "Spectral Concentration and the Sturm-Liouville Problem"
Malcolm Brown, University of Wales

October 23, 1998
Title: "The Theory of Optimal Stopping"
Ted Hill, Georgia Tech

October 30, 1998
Title: "Decay of correlations in hyperbolic dynamical systems"
Nikolai Chernov, University of Alabama, Birmingham

November 3, 1998
Title: "Picard's Theorem and its Generalization"
Min Ru, University of Houston

January 19, 1999
Title: "Polar Curves, polar varieties and their connections with equisingularity and curvature of Milnor fibers"
Bernhard Teissier, CNRS Ecole Normale Superieure

January 20, 1999
Title: "Studying Fractals with Flows"
Albert Fisher, University of Sao Paulo, Brazil

February 11, 1999
Title: "Relatively Prime Numbers and Invariant Measures under the Natural Action of SL (n,Z) on Rn"
Arnaldo Nogueira, Instituto de Matematica, Universidade Federal do Rio de Janeiro, Brazil

February 19,2000
Title: "Effect of Aggregation on Population Recovery Modeled by a Diffusion-Advection Equation"

February 25, 1999
Title: "What is the Fundamental Theorem of Algebra"
Harold Edwards, New York University-Courant Institute

February 26, 1999
Title: "Fermat's Last Theorem: What Happened"
Harold Edwards, New York University-Courant Institute

March 22, 1999
Title: "Some Asymptotic Expansions for Parabolic SPDEs"
Samy Tindel, University of Paris 13 (Villetanneuse)

April 2, 1999
Title: "Sums in L1"
Joe Diestel, Kent State

April 16, 1999
Title: "Aperiodic Dynamical Systems"
Krystyna Kuperberg, Auburn

April 30, 1999
Title: "Turbulence for Polish group actions and its applications"
Alexander Kechris, Cal Tech

1997-98
October 21, 1997
Title: "Holomorphic Dynamics in Cn"
Stefan Heinemann, University of Gottingen

November 14, 1997
Title: "Semipositone Systems"
Ratnasingham Shivaji, Mississippi State University

November 24, 1997
Title: "A dual variational approach to a class of nonlocal semilinear Tricomi
problems"
Kevin Payne, University of Miami

December 10, 1997
Title: "Recovery for an Aggregating Island Chain Model"
Victor Padron, University of Merida, Venezuela

February 6, 1998
Title: "Fermat's Last Theorem and Beal's Conjecture"
Henri Darmon, McGill University

February 20, 1998
Title: "Convective Stability of Solitary Waves on Lattices"
Robert L. Pego, University of Maryland

March 23, 1998
Title: "Sierpinski Gasket as a Martin Boundary"
Hiroshi Sato, Kyushu University

April 2, 1998
Title: "Edge K-Types and Restriction of Cohomology"
Mark Sepanski, Baylor

April 3, 1998
Title: "Combinatorial differential manifolds and matroid bundles"
Laura Anderson, Texas A&M

May 1, 1998
Title: "The Nonlinear Schroedinger Equation: Self-similar Solutions and
Scattering Theory"
Fred Weissler, University of Paris XIII

1996-97
September 16, 1996
Title: "Fredholm Alternative for Some Quasilinear Differential Operators"
Pavel Drabek, Czech Republic

November 8, 1996
Title: "Semisimplicity of Representations"
George McNinch, University of Notre Dame

November 15, 1996
Title: "Mathematician, Sculptor: Recent Works"
Helaman Ferguson, Supercomputing Research Center, Maryland

November 22, 1996
Title: "Action as a Function of Period for Ground State Solutions of Semilinear Elliptic Equations"
Y .S. Il'yasov, Steklov Mathematical Institute, Russian Academy of Sciences

January 24, 1997
Title: "The Prime Ideal Spectrum of a Noetherian Ring"
Chandni Shah, Colgate University

March 12, 1997
Title: "Rellich Inequalities"
Andreas Hinz, München University

March 28, 1997
Title: "Puig's Conjecture on Blocks of Finite Groups"

March 31, 1997
"On Matroids Representable over Both GF(4) and GF(5)"
Dirk Vertigan, LSU

April 4, 1997
Title: "Global Solutions and Self-similar Solutions of Semi-linear Evolution Equations"
Fred Weissler, University of Paris

April 24, 1997
Title: "Linearly Recurrent Systems and S-adic Systems"
Fabien Durand, Université de la Méditerranée Aix-Marseille II

May 2, 1997
Title: "Evolution Semigroups and Stability of Time-varying Systems"
Tim Randolph, University of Missouri

May 14, 1997
Title: "Semilinear Elliptic Equations"
Djairo De Figueiredo, University of Campinas, Brazil

1995-96
September 8, 1995
Title: "On Projections of High-Dimensional Measures"
Heinrich v. Weizsacker, Kaiserlautern

September 29, 1995
Title: "Topological Graph Theory and Venn Diagrams"
Peter Hamburger, Indiana-Purdue University at Fort Wayne

October 12, 1995
Title: "The Two Squares Theorem of Fermat"
W. N. Everitt, University of Birmingham (UK)

October 19, 1995
Title: "Oscillatory Radial Solutions of Semilinear Elliptic Equations"
William R. Derrick, University of Montana

November 17, 1995
Title: "Fair-Division Problems: Cake-cutting and Convexity"
Ted Hill, Georgia Institute of Technology

December 14, 1995
Title: "Equilibrium States and Families of Multipliers"
Nicolai Haydn, USC

January 26, 1996
Title: "A Survey of Dowling Lattices"
Joseph Bonin, George Washington University

February 16, 1996
Title: "Knots and Matrices"
Gail S. Nelson, Carleton College

March 15, 1996
Title: "Convective Stability and Instability of Solitary Waves"
Robert L. Pego, University of Maryland

April 3, 1996
Title: "Implicity Theorems for Quasi Self-Similar Multifractal Measures"
Toby O'Neil, University of St. Andrews

April 26, 1996
Title: "Subintegrality and Weak Subintegrality"
Leslie G. Roberts, Queen's University, Kingston, Ontario

1994-95
November 18, 1994
Title: "Diophantine Approximation: So Close, Yet So Far"
Edward B. Burger, Williams College

December 9, 1994
Title: "Elasticity of Factorization in Integral Domains"
Scott Chapman, Trinity University

January 27, 1995
Title: "K Theory and Cyclic Homology: What Are They and Why Should You Care"
Sue Geller, Texas A&M University

February 3, 1995
Title: "Semigroups with Differentiable Operations"
J. P. Holmes, Auburn University

February 10, 1995
Title: "Graphs and Groups"
Margaret Morton, University of Auckland

February 17, 1995
Title: "Modular Representations of Simple Groups"
Peter Sin, University of Florida

February 23, 1995
Title: "Harmonic Measure on Fractals"
Alexander Volberg, Michigan State University

February 24, 1995
Title: "Dynamical Systems"
James Yorke, Institute for Physical Science and Technology, University of Maryland

March 20, 1995
Title: "Fractal Geometry of Self-Avoiding Processes"
Kumiko Hatori, University of Tokyo

March 31, 1995
Title: "Flag Varieties and Exterior Powers of the Reflection Representation"
Mark Reeder, University of Oklahoma

April 7, 1995
Title: "A Survey of Uniform Homeomorphisms between Banach Spaces"
Bill Johnson, Texas A&M University

April 12, 1995
Title: "Stability and Instability in Gases and Plasmas"
Walter Strauss, Brown University