Wed, Apr 23

Analysis Seminar
Xiaoqing Li, SUNY at Buffalo
Lower bounds of the Riemann zeta function on the line 1 and GL(3)
4:00PM, 250 Math Building

In this talk, we will present a soft method deriving effective lower bounds for the Riemann zeta function on Re(s)=1, using the theory of GL(3) Eisenstein series.

Mon, Apr 28

Algebra Seminar
Padmini Veerapen, Tennessee Tech University
Regular algebras and their associated Manin universal quantum groups 
4:00PM, 250 Mathematics building

In this talk, we explore Artin-Schelter regular (henceforth, regular) algebras, noncommutative analogues of the polynomial ring. We examine some results pertaining to Manin universal quantum group of such a regular algebra. In particular, we analyze how a twist by an automorphism of an algebra may yield a 2-cocycle twist of the corresponding Manin universal quantum group. We exhibit this result in the context of the coordinate ring of the Jordan plane. Finally, we discuss a result relating Koszul regular algebras to their 2-cocycle twists using Raedschelders' and Van den Bergh's work on Manin's universal quantum groups associated with Koszul regular algebras. This is joint work with H. Huang, V. C. Nguyen, K. B. Vashaw and X.Wang that was made possible by a SQuaRE at the American Institute of Mathematics.

Tue, Apr 29

Algebra Seminar
Mee Seong Im, Johns Hopkins University
Automata, Boolean TQFT and pseudocharacters 
4:00PM, 250 Mathematics department

Finite-state automata (FSA) are important objects in theoretical computer science. I will describe how a Boolean-valued Topological Quantum Field Theory in dimension one carrying defects gives rise to an automaton. The regular language of the automaton appears through the evaluation of decorated one-manifolds. If time allows, I will explain how group characters and pseudocharacters appear in topological theory and TQFTs in one dimension with defects. Pseudocharacters are an essential tool in modern number theory. The former is joint with M. Khovanov, and the latter is joint with M.Khovanov and V. Ostrik.

Mon, May 5

Algebra Seminar
Claudiu Raicu, University of Notre Dame
Polynomial functors and stable cohomology
4:00PM, 250 Math Building

The theory of polynomial representations of the general linear group goes back to the thesis of Issai Schur at the turn of the 20th century. Such representations include the tensor, symmetric, and exterior powers of a vector space, and have been completely classified in the work of Schur when the underlying field is the complex numbers. While there has been significant progress since the work of Schur, the story over a field of positive characteristic remains largely unknown. In my talk I will describe some novel stabilization results for sheaf cohomology, and explain their connection to the study of polynomial representations / functors. This is based on joint work with Keller VandeBogert.