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.

Commutative Algebra Seminar
Speaker: Sayed Sadiqul Islam, IIT Bombay
Host: Tony J Puthenpurakal
Title: Zariski Closedness of Supports of Local Cohomology Modules
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, September 07
Venue: Room 215
Abstract: These talks are based on two recent papers, one by Katzman and Zhang and the other by Gintz and Zhang, concerning the Zariski closedness of supports of local cohomology modules in prime characteristic.

We shall show that the support of H_I^i(R/gR) is Zariski closed when R is a regular ring of prime characteristic and g is an element R . We shall also discuss an extension of this result to the case in which R has finitely many isolated singular points. Furthermore, we shall prove that if f_1 and f_2 form a regular sequence, then the support of H_I^j(R/(f_1,f_2)) is Zariski closed.

APS
Speaker: Aditya DSS, IIT Bombay
Host: Ayan Bhattacharya
Title: Growth of regularly varying branching random walks
Time, day and date: 8:15:00 AM – 9:15:00 AM, Tuesday, September 08
Venue: Conference Room
Abstract: We consider branching random walks (BRWs) with real-valued displacements having regularly varying tails, allowing the tail behavior of the displacements to vary across generations. We study the exponential growth of the BRW through its maximal position when the underlying genealogical tree is generated by a supercritical Bienaymé–Galton–Watson process with finite mean. We show that the growth exhibits a phase transition depending on the indices of regular variation of the displacement tails. We further investigate the fluctuations of the maximal position by establishing a weak limit for the appropriately normalized maximal position in the (n)-th generation.

APS
Speaker: Suraj Panigrahy, IIT Bombay
Host: Kummari Mallesham
Title: Short Second Moment of GL(2) L-Functions via Trivial Delta
Time, day and date: 10:00:00 AM – 11:00:00 AM, Tuesday, September 08
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1oeypbYUwezzQrOGejnRLBFsaBPFKwHUh/view?usp=sharing

Special Colloquium
Speaker: Pu Zhao Kow, National Chengchi University
Host: Suman Kumar Sahoo
Title: On scattering behavior of corner domains with anisotropic inhomogeneities
Time, day and date: 3:00:00 PM – 4:00:00 PM, Wednesday, September 09
Venue: Ramanujan Hall

Video Call: https://meet.google.com/ztk-bwit-ioy

Abstract: We investigate the scattering and non-scattering behavior of an anisotropic, inhomogeneous Lipschitz medium at a fixed wave number under a single incident field. By relating the anisotropic non-scattering problem to a Bernoulli-type free boundary problem, we leverage techniques from free boundary theory to show that any anisotropic medium with a Lipschitz, but not C1,α, boundary scatters all incident waves satisfying a non-degeneracy condition [1]. For degenerate incident waves, the outcomes fall into two categories [2]: In the first, we show that in two dimensions, piecewise C1 or convex penetrable obstacles with corners (and in higher dimensions, obstacles with edge points) always produce nontrivial scattering. In the second, we prove that piecewise C 1 obstacles with corners in two dimensions (or with edge points in higher dimensions) whose angles are not rational multiples also generate nontrivial scattering for any incoming wave. This is a joint work with Mikko Salo and Henrik Shahgholian.

Plancherel measure
Speaker: Dipendra Prasad, IIT Bombay
Title: Plancherel measure
Time, day and date: 5:00:00 PM – 6:15:00 PM, Friday, September 11
Venue: Room 215
Abstract: Waldspurger, J.-L. La formule de Plancherel pour les groupes p-adiques (d'après Harish-Chandra). (French) [The Plancherel formula for p-adic groups (after Harish-Chandra)] J. Inst. Math. Jussieu 2 (2003), no. 2, 235–333.