# Calendar

Nov
27
Wed
Colloquium: Elijah Liflyand (Bar-Ilan University) @ Keller 401
Nov 27 @ 3:30 pm – 4:30 pm

Speaker: Elijah Liflyand (Bar-Ilan University)
Title: A tale of two Hardy spaces

Abstract:
New relations between the Fourier transform of a function of bounded
variation and the Hilbert transform of its derivative are revealed.
If we do not distinguish between the cosine and sine transforms and consider
the general Fourier transform of $f$, direct calculations give the belonging
of the derivative $f’$ to the real Hardy space $H^1$ as a sufficient condition
for the integrability of the Fourier transform. Our analysis is more delicate.
The main result is an asymptotic formula for the {bf cosine} Fourier
transform, while much earlier known results gives an asymptotic formula
for the sine Fourier transform. The difference is achieved by assuming that
the derivative belongs to different subspaces of $H^1$. However, this tale of
each of the two subspaces were impossible if we would not have a new proof
even for the old result. The known proofs used to give strong priority just to
the sine transform. Interrelations of various function spaces are studied
in this context, first of all of these two types of Hardy spaces. The obtained
results are used for proving completely new results on the integrability
of trigonometric series.

Dec
6
Fri
Colloquium: Nate Brown (Penn State)
Dec 6 @ 3:30 pm – 4:30 pm

Speaker: Nate Brown (Penn State)

Title: Tomorrow’s STEM leaders are diverse

Abstract: Thirty years ago a radical experiment began at the University of Maryland Baltimore County (UMBC). The aim was to prepare undergraduates from underrepresented groups to be successful graduate students in STEM fields. The pillars of the program were unorthodox and the results have been stunning. In this talk I will discuss the Driving Change Initiative, funded by the Howard Hughes Medical Institute, which aims to replicate UMBC’s experiment at research institutions across the country.

Dec
20
Fri
Colloquium: Prasit Bhattacharya (U. Virginia) @ Keller 301
Dec 20 @ 2:30 pm – 3:30 pm

Speaker: Prasit Bhattacharya (U. Virginia)

Title: Stable homotopy groups of spheres, finite CW-complexes and periodic self-maps

Abstract: Patterns in the stable homotopy groups of spheres are hard to detect. However chromatic homotopy theory gives a theoretical framework which justifies existence of a robust pattern. In theory, elements of stable homotopy groups are arranged in layers called the chromatic layers (one for each natural number). However, not much is known beyond chromatic layer 1. One way to detect elements in the stable homotopy groups is via finite CW-complexes which admit special self-maps, called v_n-self-maps. This talk will introduce a new class of CW-complexes which has the potential to detect elements in chromatic layer 2 of the stable homotopy group localized at the prime 2.

Jan
22
Wed
Colloquium: Anna Puskas (Kavli Institute) @ Keller 401
Jan 22 @ 3:30 pm – 4:30 pm

Speaker: Anna Puskas (Kavli Institute for the Physics and Mathematics of the Universe)

Title: Demazure-Lusztig operators and Metaplectic Whittaker functions

Abstract:

The study of objects from Number Theory such as metaplectic Whittaker
functions has led to surprising applications of Combinatorial
Representation Theory. Classical Whittaker functions can be expressed in
terms of symmetric polynomials, such as Schur polynomials via the
Casselman-Shalika formula. Tokuyama’s theorem is an identity that links
Schur polynomials to highest-weight crystals, a symmetric structure that
has interesting combinatorial parameterizations.

Approaches to generalizing the Casselman-Shalika formula resemble the
two sides of Tokuyama’s identity. Connecting these approaches with
purely combinatorial tools motivates the search for a generalization of
Tokuyama’s theorem. This talk will discuss how the introduction of
certain algebraic tools (Demazure and Demazure-Lusztig operators) yields
such a result. We shall see how these tools can further be used to
investigate questions in the infinite-dimensional setting.

Jan
24
Fri
Colloquium: Vasu Tewari (U. Penn) @ Keller 401
Jan 24 @ 3:30 pm – 4:30 pm

Speaker: Vasu Tewari (U. Penn)

Title: Divided symmetrization and Schubert polynomials

Abstract: Divided symmetrization is an algebraic operation that takes a multivariate polynomial as input and outputs a scalar, which in many cases is a combinatorially interesting quantity. In this talk, I will describe how divided symmetrization arises in different areas of mathematics, ranging from discrete geometry, where it is intimately tied to computing volumes of permutahedra, to algebraic geometry, where it makes an appearance in the cohomology class of a certain variety.
I will then focus on the divided symmetrization of Schubert polynomials. The emphasis throughout is on the combinatorics involved.

Jan
27
Mon
Colloquium: François Greer (SUNY Stony Brook)
Jan 27 @ 3:30 pm – 4:30 pm
Feb
3
Mon
Colloquium: Liu Liu (UT Austin)
Feb 3 @ 3:30 pm – 4:30 pm

Speaker: Liu Liu (UT Austin)

Title: A Bi-fidelity method for multiscale kinetic equations with uncertainties

Abstract:

In this talk, we introduce a bi-fidelity numerical method for solving high-dimensional parametric kinetic equations. We first briefly discuss about the Boltzmann equation and its fluid dynamic limit, then introduce a bi-fidelity stochastic collocation method for its uncertainty quantification problem. By combining computational efficiency of the low-fidelity model–chosen as the compressible Euler system–with high accuracy of the high-fidelity (Boltzmann) model, our bi-fidelity approximation can successfully capture well the macroscopic quantities of solution to the Boltzmann equation in the random space. A uniform error estimate of the bi-fidelity method, based on a series of our theoretical work on hypocoercivity for the uncertain kinetic equations, will be shown. Lastly we present numerical results to validate the efficiency and accuracy of our proposed method.

Feb
7
Fri
Colloquium: Ying Wang (U. of Oklahoma)
Feb 7 @ 3:30 pm – 4:30 pm

Mathematical Analysis and Numerical Methods for an Underground Oil Recovery model

Ying Wang (University of Oklahoma)

In this talk, I will discuss a new class of entropy solutions of the modified Buckley-Leverett equation, which models underground oil recovery. This model includes a third-order mixed derivatives term resulting from the dynamical effects in the pressure difference between the two phases. Analytic study on the computational domain reduction will be provided. Strong stability preserving operator splitting method will be introduced. A variety of numerical examples will be given. They show that the solutions may have many different profiles depending on the initial conditions, diffusion parameter, and the third order mixed derivatives parameter. The results are consistent with the study of traveling wave solutions and their bifurcation diagrams.