IPDF extension seminar
Speaker: Dr. Suman Mukherjee, IIT Bombay
Host: Sanjoy Pusti
Title: Fractional Leibniz Rules for the Dunkl Laplacian
Time, day and date: 4:00:00 PM - 5:00:00 PM, Monday, April 06
Venue: Room 215
Abstract: Attached (https://drive.google.com/file/d/178K8ZVTL7Ca_2v56tEYM5RRfAI869X0I/view)

Mathematical analysis of 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 – 5:00:00 PM, Monday, April 06
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.

Mathematical analysis of reaction-diffusion equations
Speaker: Saumyajit Das, HRI
Host: Harsha Hutridurga
Title: Reaction-Diffusion equations and related topics in kinetic theory
Time, day and date: 11:00:00 AM – 12:30:00 PM, Tuesday, 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.

Topology Seminar
Speaker: Lekha Das, IIT Bombay
Host: Rekha Santhanam
Title: Equivariant operads and transfer systems
Time, day and date: 3:30:00 PM – 4:30:00 PM, Tuesday, April 07
Venue: Room 215
Abstract: We will discuss N_infinity operads and its connection to transfer systems. Using their correspondence, we will try to relate the notion of pairings of operads and compatible pairs of transfer systems.

Optimal transportation problem
Speaker: Sooraj A P, IIT Bombay
Host: Harsha Hutridurga
Title: Topics in Optimal Transportation
Time, day and date: 2:30:00 PM – 3:45:00 PM, Wednesday, April 08
Venue: Room 105
Abstract: -

Mathematics Colloquium
Speaker: Anusha Mangala Krishnan, IIT Bombay
Title: On the long-time behaviour of ancient homogeneous Ricci flows
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, April 08
Venue: Ramanujan Hall
Abstract: The Ricci flow is a means of evolving a Riemannian metric with time, with the goal of improving it, for example, to smoothen it out or to make it more round. The regularizing properties of the Ricci flow have made it a powerful tool in studying problems in geometry and topology.

In many situations, it is important to study the behaviour of the flow near singularities, that is, points where curvature becomes concentrated. Zooming into such a region gives rise to another Ricci flow solution, which then serves as a model for that singularity. Singularity models for the Ricci flow arising in this manner turn out to be ancient, that is, defined for all negative times. The simplest example of an ancient solution is the Ricci flow evolution of an Einstein metric of positive Einstein constant, which evolves by rescaling the metric linearly in time.

On a compact homogeneous space, the Ricci flow restricts to a finite-dimensional dynamical system on the space of left-invariant metrics. Within this setting, I will discuss a symmetry theorem for ancient Ricci flows, and also discuss how ancient solutions essentially emanate from Einstein metrics, possibly on a lower dimensional space.

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.

Fractional Borg–Levinson Problems
Speaker: Saumyajit Das, HRI
Host: Suman Kumar Sahoo
Title: Fractional Borg–Levinson Problem
Time, day and date: 3:30:00 PM – 4:30:00 PM, Friday, April 10
Venue: Ramanujan Hall
Abstract: In this talk, we will explore how Gel'fand spectral data can be used to determine the perturbation potential associated with the fractional Laplacian on a smooth bounded domain.