APS
Speaker: Niladri Sekhar Patra, IIT Bombay
Host: Manoj Kumar Keshari
Title: Descent problem for certificate of non-negativity on semi-algebraic sets.
Time, day and date: 5:15:00 PM – 6:15:00 PM, Monday, February 09
Venue: Ramanujan Hall
Abstract: Let R[X] (resp. Q[X]) denote the polynomial ring in n variables with real (resp. rational) coefficients. Given a finite set S in Q[X], if the quadratic module M generated by S is archimedean in R[X], then we show that the quadratic module M generated by S is Archimedean in Q[X] when Q[X]/Supp(M) is 0 dimensional, giving a partial answer to Powers' question. I will also discuss some result on saturation. This is joint work with M.K. Keshari and Debapriya Ojha.

APS
Speaker: Aratrika Pandey, IIT Bombay
Host: Ravi Raghunathan
Title: Simultaneous Khintchine theorem in local field of positive characteristic
Time, day and date: 11:45:00 AM – 12:45:00 PM, Wednesday, February 11
Venue: Ramanujan Hall
Abstract: In this talk, we focus on the convergence case of Khintchine's theorem for analytic nonplanar manifolds over local fields of positive characteristic, allowing general approximation functions $\psi$ that are not necessarily monotonic. Our approach is based on the method of counting rational points near manifolds developed by Beresnevich and Yang \cite{BY}. To address the scenario in which $\psi$ is not monotonic, we extend the function field by adjoining an appropriate root. Additionally, in the course of the proof, we establish several new results in the geometry of numbers over function fields, which we believe are of independent interest. If time permits, we will also briefly discuss the divergence case, which deals with lower bounds for counting rational points

Student Seminar
Speaker: Aditya Khambete, IIT Bombay
Host: Suman Kumar Sahoo
Title: Dependence modelling using copulas, and the extension to discrete random vectors.
Time, day and date: 2:00:00 PM – 3:00:00 PM, Wednesday, February 11
Venue: Room 215
Abstract: In this talk we will introduce the notion of copulas to model the dependence in multivariate distributions, discuss how the classical notion fails for discrete multivariate distributions, and then use ideas from Geenens (2020) to extend the idea to multivariate discrete distributions.

Mathematics Colloquium
Speaker: Girish Aras, IIT Bombay (Visiting Faculty)
Host: Radhendushka Srivastava
Title: Introduction to Causal Inference
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, February 11
Venue: Ramanujan Hall
Abstract: I will start with a few examples where confounders disrupt classical inference paradigm and motivate why a causal approach is needed. I will review the basic formalism and central ideas of causal inference such as Neyman’s potential outcomes (counterfactuals) and Don Rubin’s foundational assumptions under which causal inference is possible.

The presentation, though rigorous, should be accessible with minimal knowledge of statistics and probability theory.
 

Monge-Ampere equation
Speaker: Sooraj A P, IIT Bombay
Host: Harsha Hutridurga
Title: On the Monge-Ampere equation
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, February 12
Venue: Room 215
Abstract: We shall see a proof of the existence of solutions to the zero-boundary Dirichlet problem for the Alexandrov formulation of the Monge-Ampère equation. Later, we shall look at extensions of this to the case where the boundary data is an arbitrary continuous function.

Commutative algebra seminar
Speaker: Sayed Sadiqul Islam, IIT Bombay
Host: Tony J P
Title: F^e-modules with applications to D-modules-2
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, February 12
Venue: Ramanujan Hall
Abstract: In this talk, I will present the theory of F^e-modules, a natural extension of Lyubeznik’s F-module theory using higher powers of the Frobenius map. I will discuss a recent result by Wenliang Zhang, which extends properties of the Matlis dual of F-finite F modules to D-submodules of F^e-finite F^e-modules. Finally, I will explain how these results are applied to the Lyubeznik–Yildirim conjecture in mixed characteristic.

Algebraic groups seminar
Speaker: Shripad M. Garge, IIT Bombay
Title: Basic results on algebraic groups. I
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, February 12
Venue: Room No .215
Abstract: We begin with the first chapter of Digne-Michel, Representations of finite groups of Lie type.