Seminar on the Plancherel measure
Speaker: Ravi Raghunathan, IIT Bombay
Title: On the support of the Plancherel measure (d'après Bernstein)
Time, day and date: 5:00:00 PM – 6:15:00 PM, Monday, August 31
Venue: Ramanujan Hall
Abstract: -

Special Colloquium
Speaker: Promit Ghosal, University of Chicago
Host: Parthanil Roy
Title: Riesz-Calibrated Optimal Transport for Generalizing Treatment Effects
Time, day and date: 5:30:00 PM – 6:30:00 PM, Wednesday, September 02
Venue: Ramanujan Hall
Abstract: Randomized trials identify causal treatment effects within the trial population, but transporting these effects to a different target population requires accounting for differences in covariate distributions. We develop a new approach based on entropically regularized, semi-unbalanced optimal transport. A key observation is that standard regularized optimal transport can produce a non-vanishing bias in the induced importance weights, even as the sample size grows. We remove this bias by introducing calibration constraints into the transport problem and show that, with a growing calibration sieve, the resulting weights consistently estimate the target-to-trial density ratio, or equivalently the Riesz representer of the target expectation functional, while the transport regularization parameters remain fixed. Combined with outcome regression, this yields a doubly robust estimator that attains the semiparametric efficiency bound under suitable rate conditions, with inference obtained directly from its influence function. I will discuss the underlying statistical theory, the role of optimal transport as a regularized weighting mechanism, and numerical results illustrating robustness under weak overlap and model misspecification.

Topology seminar
Speaker: Jatin Atwal, IIT Bombay
Host: Rekha Santhanam
Title: An Introduction to Homotopy Type Theory
Time, day and date: 2:15:00 PM – 3:15:00 PM, Thursday, September 03
Venue: Room 215
Abstract: We'll give a brief overview of the subject. We'll start by looking at types, their structure, and the homotopy-theoretic properties they encode. We will talk about the two pillars of HoTT; Univalence axiom and Higher Inductive Types, and how these enable us to study homotopy theory from a synthetic viewpoint. If time permits, we'll look at the computational semantics of HoTT and how the theorems proved can be mechanically verified using proof assistants like Agda, Rocq, etc.
The talk does not assume any background, however some knowledge of homotopy theory would ease the flow of ideas.

APS
Speaker: Indrashis Gain, IIT Bombay
Host: Keshav Aggarwal
Title: Hybrid subconvexity for L(1/2 + it, sym^2 f x g)
Time, day and date: 11:00:00 AM – 12:00:00 PM, Friday, September 04
Venue: Ramanujan Hall
Abstract: In this talk, we will briefly analyze the set-up to obtain a hybrid subconvexity bound for L(s,Sym^2 f x g) which is hybrid in the aspect of level of f and pure in the aspect of t . To achieve that, we will start with an explicit review of L(s,Sym^2 f) and obtain a bound which is subconvex in the t aspect and almost convex in the aspect of the level of f. Thereafter, we shall obtain the approximate functional equation of L(s,Sym^2 f x g) at s = 1/2 + it and analyze the sums of larger lengths using the Voronoi Summation Formula.

Student Seminar
Speaker: Madhav Varshney, IIT Bombay
Host: Suman Kumar Sahoo
Title: Games in Graph Theory: Ramsey Numbers, Strategy Stealing and Potential Function Arguments
Time, day and date: 5:15:00 PM – 6:15:00 PM, Friday, September 04
Venue: Room 215
Abstract: We analyze two-player competitive edge-coloring games played on a complete graph, examining the core theoretical principles governing these graph games. We frame bounds using diagonal Ramsey numbers and apply the Erdős–Selfridge potential argument directly to the edge set of the graph to derive the asymptotic winning thresholds.