Speaker : Udit Mavinkure (University of Western Ontario)
Date:  25 March 2025, 3:00-4:00 PM
Location: Room 113 
Title: Seifert-van Kampen theorems in discrete homotopy theory

Abstract:
Discrete homotopy theory is a homotopy theory designed for studying simple graphs, detecting combinatorial, rather than topological, "holes." Central to this theory are the discrete homotopy groups which, just like their continuous counterparts, are easy to define but generally hard to compute. A discrete analogue of the Seifert-van Kampen theorem is thus a crucial tool to have in our computational toolbox. However, the version found in literature turns out to be too restrictive and is not applicable to several examples of interest. In this talk, we will state and sketch a proof of a new version that applies to a wider range of examples, and along the way, introduce some techniques with broader applicability. This talk is based on joint work with C. Kapulkin (arxiv:2303.06029).

Commutative Algebra seminar
Speaker: Samarendra Sahoo (IIT Bombay)
Host: Tony Puthenpurakal
Title: The Auslander-Reiten conjecture
Time, day and date: 4:00:00 PM, Tuesday, March 25
Venue: Ramanujan Hall
Abstract: The Auslander-Reiten conjecture, proposed in 1975, states that if Ext^i(M,M)=Ext^i(M,R)=0 for all i≥1, then the finitely generated module M over a commutative ring R with unity must be projective. Although the conjecture remains unresolved, several partial results have been established. Notably, it holds true when R is a complete intersection (CI) or a Cohen-Macaulay (CM) normal ring. In this lecture series, we will explore the work of D. Ghosh and R. Takahashi, who identified a specific class of modules that satisfy the conjecture.

Speaker: Harshit Yadav, University of Alberta, Canada

Time: 4pm to 5pm, Friday, 28th March 2025

Venue: Ramanujan Hall, Department of Mathematics

Title: Tensor category results and their applications to vertex operator algebras

Abstract: Vertex operator algebras (VOAs) and modular tensor categories (MTCs) are two central algebraic frameworks for studying two-dimensional conformal field theory. A connection between them arises through the category of modules of a VOA, which often carries a rich tensor categorical structure. In this talk, I will present some results about (modular) tensor categories and their applications to VOAs and their module categories. The focus will be on how these categorical perspectives can offer insights into the structure of VOAs. This is based on joint works with Thomas Creutzig, Robert McRae and Kenichi Shimizu.