Skip Section Navigation

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

The talks typically take place on Mondays from 4:00 to 5:00 pm in GAB 461. The talks are intended for a general audience, and everyone is encouraged to attend (including undergraduates). Refreshments are served 30 minutes before the talk in the same room as the talk.

For more information, contact Lea Beneish.

Upcoming Events 

September 29, 2025: Yingda Cheng (Virginia Tech)

Title: Low-Rank Anderson Acceleration

Abstract: In this talk, we present the low rank Anderson Acceleration (lrAA), a numerical method that directly computes low rank solutions to nonlinear equations. In many applications (e.g. nonlinear diffusion), the approximate solution, when represented as a matrix, is approximately low rank. It is challenging to design a numerical scheme for nonlinear equations that work directly with low rank. A principal challenge is that if nonlinearities are evaluated element-wise for all matrix elements then the computational savings, from quadratic to linear in the grid points per dimension, is lost.

We propose lrAA, which is based on Anderson Acceleration (AA), a well known technique for accelerating Picard iteration for fixed point problems. We couple AA with low rank truncation and cross approximations. We develop a new method for matrix cross approximation, Cross-DEIM, that uses the discrete empirical interpolation method (DEIM) based index selection to achieve effective cross approximations throughout the iterations. We show that lrAA works well for benchmark problems, such as Bratu problem and Allen-Cahn equations. This is joint work with Daniel Appelö (VT).

 

October 20, 2025: Joseph Vandehey (University of Texas, Tyler)

Title: Creating randomness in an orderly fashion

Abstract:Take the positive integers in order and concatenate them after the decimal point. The resulting number $0.1234567891011121314\cdots$ is known as Champernowne's constant. Despite being built in such a simple, mechanical way, this constant satisfies a simple test for randomness: all finite sequences of digits appear as often in Champernowne's constant as they do in the typical randomly chosen real number.

One reason for this surprising result is that decimal expansions are quite nice digitally. Every digit is as likely to occur as any other digit. Do such simple, mechanical constructions for randomness occur if we alter the expected frequencies of the digits? We will showcase some results showing that the answer is yes in many cases, as well as a new result for Bernoulli shifts of finite entropy.

 

October 27, 2025: Shawn Walker (Louisiana State University)

Title: Modeling and Numerics for the Landau--de Gennes Model of Nematic Liquid Crystals

Abstract: Liquid Crystals (LCs) are an interesting meso-phase of matter that include so-called defects that augment their behavior.  Moreover, they are easily manipulated by electric/magnetic fields.  This talk will start with an introduction/overview of nematic LCs, examples of applications, and how they are modeled.  Next, I will present some of my recent work in this area.  First, I will discuss optimal control of the time-dependent, Landau--de Gennes (LdG) model of LCs which can be used for controlled placement of defects.  Next, I will discuss cholesteric shells, which are LC droplets that have interesting optical properties.

Then, I will present recent work on developing an unfitted finite element method for the time-dependent Landau--de Gennes (LdG) model of nematic LCs within evolving domains. We demonstrate the method's capabilities through simulations of colloidal spheres moving within a nematic LC medium, which as applications in meta-materials.

 

November 17, 2025: Brendon Rhoades (University of California, San Diego)

Title: Increasing Subsequences, Matrix Loci, and Shadow play

Abstract: An increasing subsequence in a permutation $w = [w(1), \dots, w(n)]$ is a sequence $1 \leq i_1 < \cdots < i_k \leq n$ such that $w(i_1) < \cdots < w(i_k)$. Increasing subsequences in permutations play important roles in representation theory and probability. We describe a graded ring whose algebraic structure is governed by the combinatorics of increasing subsequences through the shadow line construction of X. Viennot. This ring will come from the set of $n \times n$ permutation matrices, thought of as points in matrix space. 

 

February 2, 2026: TBD

Title: TBD

Abstract: TBD

 

March 16, 2026: David Zureick-Brown (Amherst College)

Title: Beyond Fermat's Last Theorem 

Abstract: What do we (number theorists) do with ourselves now that Fermat's last theorem (FLT) has fallen? I’ll discuss numerous generalizations of FLT  --  for instance, for fixed integers $a,b,c \geq 2$ satisfying $1/a + 1/b + 1/c < 1$, Darmon and Granville proved the single generalized Fermat equation $x^a + y^b = z^c$ has only finitely many coprime integer solutions. Conjecturally something stronger is true: for $a,b,c \geq 3$ there are no non-trivial solutions. More generally, I'll discuss my subfield ``arithmetic geometry", and in particular the geometric intuitions that underlie the conjectural framework of modern number theory.

 

April 6, 2026: Cris Poor (Fordham University)

Title: TBD

Abstract: TBD

Recent Events

Date Speaker Title
2025-4-28 Parimala, Emory University Quadratic Forms from Arithmetic to Geometry
2025-4-14 Omer Ben-Neria, Einstein Institute of Mathematics, the Hebrew University In Search of Stronger Axioms
2025-4-7 Weihua Geng, Southern Methodist University Numerical methods and machine learning for the studies of biomolecular electrostatic interactions
2025-3-31 Yuan Liu, Wichita State University Sparse grid discontinuous Galerkin methods for time dependent PDEs
2025-3-17 Sheng Xu, Southern Methodist University The immersed interface method for flows around moving rigid objects
2025-3-3 Farbod Shokrieh, University of Washington Graphs in algebraic and arithmetic geometry
2025-2-17 Marianna Csörnyei, University of Chicago Embeddings into Euclidean spaces without shrinking
2025-1-13 Valentin Ovsienko, University of Champagne-Ardennes Quantum numbers? Surely you're joking, Mr. Feynman!
2024-11-18 Martin Raum, Chalmers University of Technology From Black Hole Mergers to Paramodular Forms
2024-11-11 Larry Rolen, Vanderbilt University L-functions for Harmonic Maass Forms
2024-11-4 Jiahui Chen, University of Arkansas Integrating differential operators and deep learning in biology application
2024-10-14 Ken Ribet, University of California Berkeley Why Fibonacci's Book of squares makes us dream of cubic curves
2024-10-7 Padi Fuster Aguilera, University of Colorado Boulder Modelling the world through an analyst lens
2024-9-23

Maurice Rojas, Texas A&M University

Prime Powers and Locating Roots of Equations
2024-9-16 Henri Darmon, McGill University Unique factorization domains, elliptic curves, and modular forms
2024-4-22 Sue Sierra, University of Edinburgh Enveloping algebras of infinite-dimensional Lie algebras
2024-4-15 Dinakar Ramakrishnan, Caltech An invitation to Diophantine equations, congruence numbers and beyond
2024-4-10 Hannah Larson, UC Berkeley Moduli spaces of curves
2024-3-18 Sohail Farhangi, Adam Mickiewicz University Uniform pointwise ergodic theorems via ultraproducts
2024-3-4 Xinfeng Liu, University of South Carolina Data-driven mathematical modeling, computation and experimental investigation of dynamical heterogeneity in breast cancer
2023-11-13 Shuang Liu, UNT Computational moving boundary problems
2023-10-23 Wesley Perkins, Lyon College Modulational and subharmonic dynamics of periodic waves
2023-10-9 Natasha Sharma, UT El Paso Unconditional energy stability and solvability for a co-interior penalty method for a sixth-order Cahn-Hilliard type equation modeling microemulsions
2023-9-18 Tamara Kucherenko, CUNY Ergodic theory on coded shifts
2023-9-6 Paco Villaroya, Santa Clara University A characterization of compactness for singular integral operators