Probability and Statistics Seminar
Speaker: Dr Matthew Parry, Associate Professor in Statistics, University of Otago, New Zealand
Host: Siuli Mukhopadhyay
Title: Finding Things in High Dimensions
Time, day and date: 12:00:00 PM – 1:00:00 PM, Monday, September 28
Venue: Ramanujan Hall 
Abstract: Data scientists and statisticians look for meaningful patterns in data. But finding those patterns can become surprisingly difficult when data have hundreds, thousands, or even millions of dimensions. In this talk, I'll explore how we can group documents and images, find biomarkers for disease, and recommend movies and TV series to viewers.

Special Talk
Speaker: Prof. R.V Gurjar
Host: Krishnan Sivasubramanian
Title: The Jacobian Problem
Time, day and date: 3:00:00 PM – 4:00:00 PM, Monday, September 28
Venue: LH 302
Abstract: Recently, Alpoge, Matthew, and Claude Fable gave a surprising counterexample to the Jacobian Problem in three or more variables. In this lecture we will first start with easy observations about the Jacobian Problem. Later we will discuss interesting special results proved by many mathematicians like S.S. Abhyankar, Abhyankar Gurjar Inversion Formula, Applegate-Onishi, Bass-Connell-Wright, Jagzev, T. T. Moh, A. Magnus, Nakai-Baba, S. Wang, S. Kaliman etc. Due to lack of time no proofs will be discussed. We will suggest possible special results for young mathematicians to try to prove. We will discuss results by many mathematicians for the 2-variable Jacobian Problem.

APS
Speaker: Kshitij Sinha, IIT Bombay
Host: Harsha Hutridurga
Title: Spectral Problems and Fine Properties of Solutions in Periodic Homogenization
Time, day and date: 4:30:00 PM – 5:30:00 PM, Monday, September 28
Venue: Ramanujan Hall
Abstract: In this talk, I will discuss spectral problems for the Laplacian and the Bilaplacian in perforated domains with various boundary conditions, as well as fine properties of solutions to divergence-form elliptic PDEs, in the context of quasi-periodic and almost-periodic homogenization.

First, I will present theoretical results on the asymptotic behaviour of eigenvalues of the Bilaplacian, motivated by a work of Nandakumaran. Next, I will discuss a numerical study of the Neumann eigenvalues of the Laplacian in perforated domains, motivated by a work of Vanninathan. Finally, I will derive doubling inequalities for divergence form elliptic equations with quasi-periodic and almost-periodic coefficients.

APS
Speaker: Aditya Dwivedi, IIT Bombay
Host: Manoj K Keshari
Title: A cotriple perspective on the HKR theorem
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, September 28
Venue: Room 113
Abstract: The Hochschild-Kostant-Rosenberg (HKR) theorem states that for a smooth commutative algebra A over a field k, the Hochschild homology of A is isomorphic to the exterior powers of the module of Kahler differentials:

HHn(A,A) \iso \omega^n A/k.

In this talk I will present a cotriple perspective on this result. The free-forgetful adjunction between commutative k-algebras and k-modules gives rise to a cotriple resolution of A by polynomial algebras, and applying the Hochschild complex levelwise produces a first-quadrant spectral sequence converging to HH*(A,A). Its E2-page is given by the homology of the exterior powers of the cotangent complex, so the HKR isomorphism is equivalent to the vanishing of the higher Andre-Quillen homology of A.This forces the spectral sequence to collapse at E2, recovering the HKR isomorphism and making explicit the role of smoothness in the proof.

Plancherel Measure
Speaker: Devadatta Hegde, School of Mathematics, TIFR
Host: Ravi Raghunathan
Title:  Plancherel measure for $p$-adic groups following Harish-Chandra
Time, day and date: 5:00:00 PM – 6 :15:00 PM, Monday, September 28
Venue: Room 215
Abstract: -