Mon, Oct 19
Algebra Seminar
Mark Shimozono (Virginia Tech)
Realizations of equivariant homology of affine Grassmannians in symmetric functions
4:00 PM, 250 Math Building
It has been known since the 1970s that the cohomology ring of the Grassmannian is a quotient of the ring of symmetric functions with the Schubert basis indexed by certain Schur functions, allowing the computation of intersection numbers for Schubert classes via combinatorics. Analogously we will describe symmetric function realizations of the equivariant homology and cohomology of affine Grassmannians of reductive algebraic groups of classical type.
Mon, Oct 19
Applied Mathematics Seminar
Baofeng Teng, The University of Texas Rio Grande Valley
Soliton solutions on an elliptic background
4:00 PM, 122 Mathematics Building
In this talk, we will present a framework to construct various soliton solutions for integrable PDEs on an elliptic background. First, we will establish elliptic analogues of AKP, BKP, CKP and DKP hierarchies, as well as their tau functions expressed by Weierstrass elliptic functions. Then by the Kadomtsev–Petviashvili (KP) reduction method, breather and rogue wave solutions on an elliptic background can be derived systematically. This is a joint work with my Ph.D student: Changyan Shi.
Tue, Oct 20
What is...? Seminar
Johanna Mangahas
TBA
4:00 PM, 250 Mathematics Building
TBA
Wed, Oct 21
Analysis Seminar
Youness Lamzouri, IECL, Université de Lorraine
A Hilbert space approach to the zeros of the Riemann zetafunction and applications
4:00 PM, 210 Mathematics building
The Riemann Hypothesis asserts that all non-trivial zeros of tRiemann zeta function lie on the critical line Re(s)=1/2. In the absence of a proof of the Riemann hypothesis, a fundamental problem has been to determine what proportion of the zeros can be shown to lie on the critical line. In this talk, I will introduce a new Hilbert space approach that establishes a direct connection between Montgomery’s pair correlation method and the study of zeros of the Riemann zeta function on the critical line. This approach yields a new conceptually simpler proof that more than two thirds of the zeros are simple and lie on the critical line. I will also discuss several further applications of this method.
Thu, Oct 22
Colloquium
Sahana Balasubramanya (Lafayette College)
Extending acylindricity to higher rank- an overview
4:00 PM, Mathematics Building
I will present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-) acylindrically on finite products of hyperbolic spaces. This work (joint with T. Fernos) is inspired by the classical theory of S-arithmetic lattices and that of acylindrically hyperbolic groups. I will start with the motivation for studying these groups in this talk, and cover some results we have proved that highlight this duality.