Topology Seminar
Speaker: Udit Mavinkurve, IIT Bombay
Host: Rekha Santhanam
Title: Quasicategories vs Segal spaces, Part 1
Time, day and date: 11:45:00 AM – 12:45:00 PM, Thursday, April 09
Venue: Room 215
Abstract: This is Part 1 in a series of 4 expository talks that will culminate in Joyal and Tierney's proof of two Quillen equivalences between the Joyal model structure for quasicategories and the Rezk model structure for complete Segal spaces, both of which present the homotopy theory of (oo,1)-categories.

In this first talk, we will introduce (oo,1)-categories, where they come from, why they are useful, and look at various models of (oo,1)-categories.

Commutative Algebra seminar
Speaker: Kaushik Khamari, IIT Bombay
Host: Tony Puthenpurakal
Title: On Cohen-Macaulay Property of Affine Semigroup Rings II
Time, day and date: 3:00:00 PM - 4:00:00 PM, Thursday, April 09
Venue: Ramanujan Hall
Abstract: In this talk, we discuss the Cohen-Macaulay property of affine semigroup rings. In the process, we describe the relationship between local cohomology modules of these rings and the homology of certain simplicial complexes. As an application, we present a proof of Hochster's Theorem, which asserts that normal semigroup rings are Cohen-Macaulay. We follow the paper of N.V. Trung and L.T. Hoa, "Affine Semigroups and Cohen-Macaulay Rings generated by monomials.

Algebraic groups seminar
Speaker: Patrick Polo, IIT Bombay
Host: Shripad Garge
Title: Harish-Chandra Series
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, April 09
Venue: Room No .215
Abstract: We will finish the proof of Mackey formula. We will then prove that Harish-Chandra series forms a partition of the set of irreducible representations.

Reaction-Diffusion equations
Speaker: Saumyajit Das, HRI
Host: Harsha Hutridurga
Title: Reaction-Diffusion equations and related topics in kinetic theory
Time, day and date: 4:00:00 PM – 5:30:00 PM, Thursday, April 09
Venue: Ramanujan Hall
Abstract: We consider various Reaction-Diffusion equations with finitely many unknowns and prove related existence results. We show how to extend these techniques to address kinetic models such as the fragmentation coagulation models where we have infinitely many unknowns.

Graphicality of prime gap graphs
Speaker: Mr. Martand Puri, IIT Bombay
Host: Keshav Aggarwal
Title: On the Vijay-Tripathi theorem
Time, day and date: 5:30:00 PM – 6:00:00 PM, Thursday, April 09
Venue: Room 113
Abstract: We present proof of the Vijay-Tripathi theorem, which is a simplification of the Erdos-Gallai criterion for graphicality of a sequence.

Graphicality of prime gap graphs
Speaker: Mr. Nirav Bhattad, IIT Bombay
Host: Keshav Aggarwal
Title: An explicit upper bound for logarithmic derivative of zeta at positive real part
Time, day and date: 6:00:00 PM – 6:30:00 PM, Thursday, April 09
Venue: Room 113
Abstract: We present an explicit bound of logarithmic strength for the logarithmic derivative of the Riemann zeta function at positive real part.