Fall 2019





Sep 9


Texas Tech

Riemann zeta and multiple zeta values

In this talk, we bring into perspective the famous Riemann zeta function and its natural generalization, the multiple zeta functions. We focus more on the evaluations of such objects at positive integers. The techniques used in these evaluations rely on the properties of some special functions.
Although they look rather simple, it turns out that the single and multiple zeta values play a very important role at the interface of analysis, number theory, geometry and physics with applications ranging from periods of mixed Tate motives to evaluating Feynman integrals in quantum field theory.
The talk should be accessible to non specialists and graduate students.

Sep 16


UT Tyler

Continued fractions, normality, and the difficulty of multiplying by 2

An expansion of a number is said to be normal if every finite string of digits in the expansion appears with a particular limiting frequency. For baseb expansions, the required frequency of a ndigit string should be b^{n}. For continued fractions, the required frequency of a string is determined by the GaussKuzmin statistics. It's known that certain operations preserve normality. For baseb expansions, multiplication and addition by nonzero rationals preserve normality. This is in part because the complexity of these operations in baseb is negligible. An exact notion of "low complexity operation" for continued fraction expansions has not been formulated, and even multiplication by 2 is a vastly more intricate procedure for continued fractions than baseb expansion, we nonetheless will show that multiplication and addition by nonzero rationals preserves normality for continued fraction expansions.

Sep 23


CCNY

Computability of thermodynamic invariants on shift spaces beyond SFTs

We consider shift maps on finite alphabet shift spaces and discuss questions concerning the computability (in the sense of computable analysis) of relevant thermodynamic invariants such as entropy, topological pressure and residual entropy. These questions have been recently studied for subshifts of finite type (SFTs) and their factors (sofic shifts) by Spandl, Hertling and Spandl, and Burr, Schmoll and Wolf. In this talk we consider possible extensions to more general classes of shift spaces including Sgap shifts, betashifts and bounded density shifts. Several positive computability results will be presented but we also show that for certain shifts even the entropy is not computable.
The results presented in this talk are part of an ongoing collaboration with M. Burr (Clemson), S. Das (NYU) and Y. Yang (Virginia Tech).

Sep 30


UNT

Numerical approximations of systems related with phase
field models and fluids

An approach for solving interface problems is the diffuse interface theory, which was originally developed as methodology for modeling and approximating solidliquid phase transitions in which the effectsof surface tension and nonequilibrium thermodynamic behavior may be important at the surface. The diffuse interface model describes the interface by a mixing energy represented as a layer of small thickness. This idea can be traced to van der Waals, and is the foundation for the phasefield theory for phase transition and critical phenomena. Thus, the structure of the interface is determined by molecular forces; the tendencies for mixing and demixing are balanced through the nonlocal mixing energy. The method uses an auxiliary function (socalled phasefield function) to localize the phases, assuming distinct values in the bulk phases (for instance 1 in a phase and 1 in the other one) away from the interfacial regionsover which the phase function varies smoothly.
During the talk I will present the main ideas to approximate the CahnHilliard model, a classical Phase field model, introducing different numerical schemes and showing the advantage and disadvantages of each scheme. The key point is to try to preserve the properties of the original models while the numerical schemes are efficient in time.
Finally, I will show how these ideas for designing numerical schemes to approximate phasefields models can be extended to other applications.

Oct 7





Oct 14


UNT

Numerical Approaches and Applications for Uncertainty Quantification.

Uncertainty is inevitable in computerbased simulations. To provide more reliable predictions for the behavior of complex systems or optimal designs for the large structures, understanding and quantifying the uncertainty in simulations is critical. In this talk, we will focus on two of the main aspects of uncertainty quantification (UQ): model form UQ (backward UQ or model calibration) and application of UQ to material design. Specifically, for model form UQ, observations are available and physical constraints are incorporated into model correction process to enforce the important physical properties of the underlying system. The estimation of both model output and model parameters can be improved. For the application of UQ, we propose a robust inverse design procedure for the optimal morphology of nanoparticles in Plasmonics. Specifically, we use a global sensitivity analysis method to identify the important random variables and consider the nonimportant ones as deterministic, and consequently reduce the dimension of the stochastic space. In addition, we apply the generalized polynomial chaos expansion method for constructing computationally cheaper surrogate models to approximate and replace the full simulations.

Oct 21


Williams College and NSF

Weak mixing in infinite measure

The weak mixing notion has played an important role in the ergodic theory of finite measurepreserving transformations, and there are several interesting, and different, characterizations of this notion. In infinite measure many of these characterizations are not equivalent. Some go back to a 1963 paper of Kakutani and Parry but there are many recent ones. We will discuss these various notions including recent progress and open questions.

Oct 28





Nov 4


University of York

TBA


Nov 11





Nov 18


Bowdoin College

TBA


Nov 25


UT Dallas

Million Dollar Problem  Poincare Conjecture

In this talk, we will describe the only millennium problem solved so far: Poincare Conjecture. We will talk about the background of the problem, and give an overview of Perelman's solution via Ricci Flow. In particular, without going into technical details, we will describe the Thurston's Geometrization Conjecture which gives the complete classification of 3manifolds.

Dec 2










Spring 2020





Jan 27





Feb 3





Feb 10





Feb 17


Harvard University

TBA


Feb 24


Muhlenberg University

TBA


Mar 2





Mar 16





Mar 23





Mar 30





Apr 6





Apr13





Apr 20





Apr 27




