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.

APS
Speaker: Bittu Singh, IIT Bombay
Host: Rekha Santhanam
Title: On Equivariant Formality of G-equivariant Sapces and Maps
Time, day and date: 10:00:00 AM – 11:00:00 AM, Thursday, September 10
Venue: Ramanujan Hall
Abstract: Triantafillou and Scull developed an equivariant rational homotopy theory in which the rational $G$-homotopy type of a simply $G$-connected space is encoded by a suitable functor taking values in commutative differential graded algebras (CDGAs). When the rational $G$-homotopy type of a $G$-space is completely determined by the associated cohomology diagram, the space is called equivariantly formal. This perspective naturally leads to the study of formal maps, namely maps whose rational homotopy-theoretic information is, up to the appropriate notion of equivalence, determined by their induced maps in cohomology. In this talk, we discuss formality of spaces and maps in the equivariant setting. 

Algebraic Groups Seminar
Speaker: Sabyasachi Dhar, IIT Bombay
Host: Shripad M. Garge
Title: F-rank and the duality functor
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, September 10
Venue: Room 215
Abstract: F-rank and the duality functor from Digne-Michel, Chapter 7

Student Seminar
Speaker: Omkar Ramdas, IIT Bombay
Host: Suman Kumar Sahoo
Title: Putting on Your Thinking Cap: How to Get A Head in a Guessing Game
Time, day and date: 3:30:00 PM – 4:30:00 PM, Friday, September 11
Venue: Ramanujan Hall
Abstract: You might have heard about the Colored hats guessing game where 'n' players, each wearing a randomly assigned black or white hat, must attempt to guess their own hat color without communicating. A simple strategy easily yields a 50% success rate, so the real question is "Can we improve this success rate significantly?". We will demonstrate how to improve these odds for a large, fixed 'n' by translating the game into a structural problem on the Boolean hypercube $\{0,1\}^n$. We will then use some basic probabilistic methods to get better strategy which will "almost" surely make you win. If time permits, we will see its connections with Hamming codes.

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.

IPDF Progress Seminar
Speaker: Dr. Utsav Dewan, IIT Bombay
Host: Mayukh Mukherjee
Title: Boundary behaviour of eigenfunctions and superharmonic functions on harmonic manifolds of purely exponential volume growth
Time, day and date: 3:00:00 PM – 4:00:00 PM, Wednesday, September 16
Venue: Ramanujan Hall
Abstract: On X, a non-positively curved harmonic manifold of purely exponential volume growth, of dimension at least 3, we study certain quantitative aspects of the boundary behaviour of eigenfunctions and superharmonic functions. We first focus on complex-valued eigenfunctions with eigenvalues lying outside the L^2-spectrum of the Laplace-Beltrami operator and obtain the almost everywhere existence of weighted non-tangential limits, sharp Hausdorff dimension and Hausdorff measure estimates of the boundary exceptional sets for radial limits. Then in the second part, we shift our attention to non-tangential and tangential boundary behaviour of positive superharmonic functions. Most of our results are new even for the homogeneous setting of rank one Riemannian symmetric spaces of non-compact type and Damek-Ricci spaces. Our arguments are based on potential theory adapted to the intrinsic Gromov hyperbolic geometry of X.

Seminar
Speaker: Dr. Smaranika Bera, Department of Mathematics Indian Institute of Engineering Science and Technology, Shibpur
Host: Siuli Mukhopadhyay
Title: Some Problems Related to Nonparametric Inference and Stochastic Ordering
Time, day and date: 4:30:00 PM – 5:30:00 PM, Wednesday, September 16
Venue: Online (https://meet.google.com/ywy-cbhx-eeg)
Abstract: My research work can be broadly divided into two parts. The first part focuses on the inferential aspects of nonparametric ageing classes of life distributions. Particularly in this side I have worked on hypothesis testing problems related to testing exponentiality against different non-monotonic ageing alternatives and on goodness of-fit assessment. The second part deals with selected probabilistic problems in reliability theory. This side mainly involves stochastic ordering, characterization of ageing classes and related probabilistic methods. In this presentation, I shall discuss two selected problems, one from each of these two areas. The first problem is from the inferential side and concerns a two-sample nonparametric testing problem for Second-Order Stochastic Dominance (SSD). We develop a large-sample testing procedure based on U-statistic theory. Since conventional U statistic methods can involve considerable computational effort, we consider alternative approaches based on Jackknife Empirical Likelihood (JEL), Adjusted JEL (AdJEL), and Balanced Adjusted JEL (BaJEL). The performance of these methods is studied through simulation experiments and their practical usefulness is demonstrated using real-life data.
The second problem comes from the probabilistic side and concerns stochastic ordering of order statistics from heterogeneous generalized Gompertz distributions. Here, we consider independent but non-identically distributed generalized Gompertz random variables. One of the main advantages of this distribution is its flexibility in describing different ageing behaviours, including increasing, decreasing and bathtub-shaped hazard rates. Using vector majorization techniques, we establish a variety of stochastic ordering results for order statistics from heterogeneous generalized Gompertz populations.
Although the main focus is on extreme order statistics, the results are also extended to general kth order statistics. We further study multiple-outlier models and obtain stochastic ordering results for extreme order statistics from two independent collections of generalized Gompertz random variables. Stronger ordering results are also obtained for second-order statistics.
Through these two problems, the presentation highlights how both nonparametric inference and stochastic ordering can be used to address interesting and practically relevant questions in reliability theory and survival analysis.

PDF extension seminar
Speaker: Dr. Cyril Jacob, IIT Bombay
Host: Ronnie Mani Sebastain
Title: The Interpolation Problem on Hirzebruch Surfaces
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, September 17
Venue: Ramanujan Hall
Abstract: The interpolation problem for plane curves on $\mathbb P^2$ has been extensively studied, with the SHGH Conjecture providing a conjectural answer. An analogous interpolation problem for curves on Hirzebruch surfaces $\mathbb F_e=\mathbb P(\mathcal O_{\mathbb P^1}\oplus\mathcal O_{\mathbb P^1}(-e))$ was studied by Antonio Laface, who proposed a conjecture closely related to the SHGH Conjecture. In this talk, we examine versions of the SHGH Conjecture for Hirzebruch surfaces. Finally, we prove this conjecture when the number of very general points satisfies $r\leq e+5$. This is joint work with Ronnie Sebastian.

APS
Speaker: Debapriya Ojha, IIT Bombay
Host: Manoj Kumar Keshari
Title: Positive Polynomials on a Strip
Time, day and date: 12:00:00 PM – 1:00:00 PM, Friday, September 18
Venue: Room 113 (https://meet.google.com/vid-bpnc-ujc)
Abstract: Let F be a subfield of the real numbers R. Let S = {g1, . . ., gs} ⊂ F[x1, . . . , xn] be a finite set of polynomials in n variables and let K_S be the basic closed semialgebraic set generated by the non-negativity of S in R^n. Also, let U ⊂ F[t] be the natural choice of generators of a noncompact basic closed semialgebraic set K_U in R with boundary ∂K_U ⊂ F. We show that f ∈ F[x1, . . . , xn, t] > 0 on K_S × K_U and fully m-ic on K_S implies f belongs to the preordering of F[x1, . . . , xn, t] generated by S, U and non-negative elements of F.

Spectral geometry
Speaker: Anusha Bhattacharya, IISER Mohali
Host: Saikat Mazumdar
Title: Anusha Bhattacharya, IISER Mohali
Time, day and date: 3:00:00 PM – 4:00:00 PM, Friday, September 18
Venue: Online (https://us06web.zoom.us/j/84551518386?pwd=7Kv5mWUygLqQPCDE7dpoBq3vMutUbB.1)
Meeting ID: 845 5151 8386
Passcode: 607090
Abstract: A central problem in spectral geometry is to determine how the eigenvalues of the Laplacian on a Riemannian manifold depend on geometric quantities, such as curvature, diameter, volume, and injectivity radius. While uniform spectral estimates are well understood under sectional curvature bounds, considerably less is known when only Ricci curvature bounds are imposed. We address this question by deriving uniform estimates and spectral approximation results for the eigenvalues of the Laplacian using discretizations of the Riemannian manifold.
We consider the class of closed Riemannian n-manifolds with Ricci curvature and injectivity radius bounded below and diameter bounded above. In this class, we prove uniform estimates for the eigenvalues of the Hodge Laplacian and connection Laplacian acting on differential forms. This extends earlier work of Dodziuk and Lott, which required sectional curvature bounds. As an application, we derive a uniform upper bound on the spectral gap for non-compact manifolds with Ricci curvature bounded below. Under the additional assumption of an upper Ricci curvature bound, we consider weighted proximity graphs constructed from sufficiently dense points on the manifold. We then establish uniform convergence of the spectrum of the associated normalized graph Laplacians to those of the Laplace-Beltrami operator.
We further study compact Riemannian manifolds with smooth cylindrical boundary satisfying the same geometric bounds. On these manifolds, we construct graph Laplacians from sufficiently dense point samples on appropriate truncations and establish uniform convergence of the spectrum of the truncated graph Laplacian to the Dirichlet spectrum of the Laplace-Beltrami operator.

APS
Speaker: Hamidul Ahmed, IIT Bombay
Host: Bata Krishna Das
Title: Isomorphism Problems for Multiplier Algebras of CNP Dirichlet Series Kernels
Time, day and date: 10:00:00 AM – 11:00:00 AM, Tuesday, September 22
Venue: Ramanujan Hall
Abstract: In this talk, we study isometric and algebraic isomorphisms between multiplier algebras of reproducing kernel Hilbert spaces associated with complete Nevanlinna–Pick (CNP) Dirichlet series kernels. We consider a broader class of CNP Dirichlet series kernels, namely those whose frequency data contain generating subtuples. For this class, we establish a connection between the multiplier algebra, the geometric structure of the associated multiplier variety, and the arithmetic structure of the frequency data. We then obtain a complete classification of both isometric and algebraic isomorphisms between the corresponding multiplier algebras.

APS
Speaker: Jayant Sharma, IIT Bombay
Host: Manas Rachh
Title: Analysis of Laplace and Helmholtz Equations in Unbounded Domains: Solvability and Radiation Conditions
Time, day and date: 3:00:00 PM - 4:00:00 PM, Tuesday, September 22
Venue: Ramanujan Hall
Abstract: Solving elliptic partial differential equations (PDEs) in unbounded domains introduces significant challenges regarding the existence and uniqueness of solutions. Without appropriate asymptotic conditions at infinity, solutions may fail to exist or may exhibit arbitrary behaviour, leading to a loss of uniqueness.

This seminar presents an analysis of the Laplace and Helmholtz equations within unbounded domains.

We begin by solving the exterior problem for a unit circle using the separation of variables to establish foundational intuition. These concepts are then generalized to an unbounded domain in R²/R³, followed by a rigorous proof of the uniqueness of the solution for the Laplace equation. Furthermore, we will see solutions to the Helmholtz equation are analytic and this property will be used to prove Rellich's lemma which gives the uniqueness of the solution for the Helmholtz equation.

APS
Speaker: Imran Hussain, IIT Bombay
Host: Saikat Mazumdar
Title: Branson's Q curvature, rigidity, compactness and uniqueness.
Time, day and date: 4:15:00 PM - 5:15:00 PM, Tuesday, September 22
Venue: Ramanujan Hall
Abstract: On a Riemannian manifold (M,g), Branson defined a curvature known as Q-curvature. Analogous to the classical Yamabe problem for scalar curvature, there is a program for the Q-curvature, we shall discuss the rigidity, compactness, and uniqueness for the Q-curvature problem.

APS
Speaker: Manish Prasad, IIT Bombay
Host: Prachi Mahajan
Title: Castelnuovo Mumford Regularity Theorem.
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, September 23
Venue: Room 105
Abstract: The m-regularity of a coherent sheaf on P^n is an important tool for the construction of the Quot scheme. In this presentation we will prove the Castelnuovo-Mumford regularity theorem, which allows us to conclude the m-regularity of some special coherent sheaves. 

More precisely, we will prove the following:
Given any non-negative integers p, n, we show that there exists a polynomial F_p,n with integral coefficients such that for any coherent subsheaf G of p copies of the structure sheaf on P^n, G is F_p,n(a_0, a_1, a_2, ..., a_n)-regular, for suitable integers a_0, a_1, ..., a_n.

CACAAG Seminar
Speaker: Dr. Charu Goel, IIM, Mumbai.
Host: Madhusudan Manjunath
Title: Real Algebraic Geometry around Hilbert's 17th Problem (Sums of Squares).
Time, day and date: 10:30:00 AM – 11:30:00 AM, Thursday, September 24
Venue: Ramanujan Hall
Abstract: -

APS
Speaker: Harshita Agarwal, IIT Bombay
Host: Ashish Das
Title: -
Time, day and date: 3:30:00 PM – 4:00:00 PM, Thursday, September 24
Venue: Conference Room
Abstract: -

APS
Speaker: Neeraj Rawat, IIT Bombay
Host: Harsha Hutridurga
Title: Free Boundary Problems and Homogenization.
Time, day and date: 3:30:00 PM – 4:30:00 PM, Thursday, September 24
Venue: Ramanujan Hall
Abstract: The talk covers homogenization of elliptic and parabolic obstacle problems with oscillating coefficients: convergence of coincidence sets and free boundaries under homogenization, a 1D example showing free-boundary homogenization can fail with a fixed obstacle, and a quantitative Hausdorff-distance rate of convergence for the coincidence sets. This is then extended to the one-phase Stefan problem, recast as an evolution variational inequality, with analogous homogenization and convergence results.

Algebraic Groups Seminar
Speaker: Ankita Parashar, IIT Bombay
Host: Shripad M. Garge
Title: -
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, September 24
Venue: Room 215
Abstract: Ch. 7, focusing on Section 7.4, and define the Deligne-Lusztig induction

Students' Seminar
Speaker: Samit Pandit, IIT Bombay
Host: Suman Kumar Sahoo
Title: An elementary proof of Grothendieck's Non-Vanishing Theorem and its geometric consequences
Time, day and date: 5:15:00 PM – 6:00:00 PM, Thursday, September 24
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1cH5Hx1S4KOvezvZXP8DSxi3VzzYg0Pca/view?usp=sharing 

APS
Speaker: Soumyajit Acharyya, IIT Bombay
Host: Chandan Biswas
Title: Besicovitch Compression and a Quantitative Failure of Endpoint Fourier Restriction
Time, day and date: 10:00:00 AM – 11:00:00 AM, Friday, September 25
Venue: Online (https://us06web.zoom.us/j/82255856730?pwd=55smRtn0conmA2vRyLwGSKmNQxVEr4.1)
Meeting ID: 822 5585 6730
Passcode: 116874
Abstract: A classical theorem of Beckner, Carbery, Semmes, and Soria states that the Fourier restriction operator for the sphere does not satisfy the restricted weak-type estimate at the conjectured endpoint. Their proof uses the Besicovitch compression phenomenon and proceeds by contradiction. As a result, it reveals little about how badly the estimate fails. We develop a general framework that converts Besicovitch compression into a quantitative failure at an endpoint. Given a family of sets that compresses, our framework produces an explicit set that violates the bound, with a rate governed by the amount of compression. The rate is sharp within the admissible family of sets. We apply this to the sphere and the paraboloid and construct a deterministic sequence of sets along which the restricted weak-type inequality degrades at an explicitly computed rate. We will also discuss why our construction does not provide blowup for the moment curve in dimensions three and higher, where the (much stronger) restricted strong-type bound is known to hold at the endpoint.

APS
Speaker: Surajit Pal, IIT Bombay
Host: Debanjana Mitra
Title: Characterization of the Reachable Space for Coupled Parabolic System with Boundary Controls.
Time, day and date: 2:30:00 PM – 3:30:00 PM, Friday, September 25
Venue: Ramanujan Hall
Abstract: We are interested in the characterization of the reachable space of a coupled parabolic system with boundary controls. For uniform diffusion coefficients, we have shown that the reachable space is a certain Bergman Space. Further, using this result, we have derived local reachability results for a coupled nonlinear system. For distinct diffusion coefficients, using Fourier series technique, we have obtained a partial characterization of the reachable space for a coupled parabolic linear system.

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: -

APS
Speaker: Lal Bahadur Sahu, IIT Bombay
Host: Sandip Singh
Title: Some infinite families of arithmetic symplectic hypergeometric groups.
Time, day and date: 10:00:00 AM – 11:00:00 AM, Tuesday, September 29
Venue: Room 215
Abstract: In this talk, we construct some of the very first examples of infinite families of arithmetic symplectic hypergeometric groups that do NOT satisfy the arithmeticity criterion of Singh and Venkataramana.
For example, we show that the hypergeometric groups associated to the pairs of polynomials $(x-1)^4P_m(x^{9})$ and $(x^4+x^3+2x^2+x+1)Q_m(x^{9})$, where $P_m$ and $Q_m$ are integral polynomials of degree $2m$ such that the corresponding pair determines a Zariski dense symplectic hypergeometric group, are arithmetic in $\Sp(18m+4)$ for any integer $m\in\N$.

APS
Speaker: Adarsh Gupta, IIT Bombay
Host: Sudarshan R. Gurjar
Title: Line bundle restrictions to Hyperplane sections and their connections to first homology on Affine Varieties.
Time, day and date: 12:30:00 PM – 1:30:00 PM, Tuesday, September 29
Venue: Room 105
Abstract: The broad aim of the talk is to understand line bundles on affine varieties and their restrictions to hyperplane sections. We examine connections between torsion line bundles and units in the coordinate ring and also make connections of these objects with the first homology groups.

APS
Speaker: Amal Das, IIT Bombay
Host: Saikat Mazumdar
Title: Compactness and Stability for the Hardy-Sobolev equation.
Time, day and date: 2:30:00 PM – 3:30:00 PM, Tuesday, September 29
Venue: Ramanujan Hall
Abstract: We will study the Hardy-Sobolev equation with full boundary singularities and critical growth. We will show that blow-up solutions concentrate at a finite number of points on the boundary of the domain, and also show the compactness and stability of the solutions.

APS
Speaker: Amanpreet Singh, IIT Bombay
Host: Saurav Bhaumik
Title: Moduli Field Vs. Field of Definition of projective schemes over $\mathb{C}$
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, September 29
Venue: Ramanujan Hall
Abstract: In this seminar, we study the moduli field $M(X)$ of projective schemes $X$ and the question of when a projective scheme can be defined over a finite extension of its moduli field.
we study this question for projective schemes whose canonical sheaf is ample or anti-ample, and prove the following main theorem: Let $X$  be a smooth, irreducible projective scheme of finite type over $\mathbb{C}$ and the canonical sheaf $\omega_X$ or the anti-canonical sheaf $\omega_X^{-1}$ is ample, then X can be defined over a finite extension of its moduli field M(X). 
As an immediate consequence, we recover the theorem of Hammer and Herrlich: a smooth projective curve over $\mathbb{C}$ of genus $g \geq  2$ can be defined over a finite extension of its moduli field.

APS
Speaker: Pallab Kumar Sinha, IIT Bombay
Host: Siuli Mukhopadhyay
Title: Discrete Time Chain Binomial Model for Infectious Disease Transmission.
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, September 29
Venue: Conference Room
Abstract: -

APS
Speaker: Pooja Lamba, IIT Bombay
Host: Monika Bhattacharjee
Title: -
Time, day and date: 11:30:00 AM – 12:30:00 PM, Tuesday, September 29
Venue: Ramanujan Hall
Abstract: -

APS
Speaker: Sayantan Sinha, IIT Bombay
Host: Debraj Das
Title: Large Language Models, Statistics, and Watermarking 
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, September 30
Venue: Conference Room
Abstract: In this seminar presentation we examine the mathematical and statistical principles underlying modern Large Language Models (LLMs), tracing their evolution from foundational probabilistic language modeling to transformer architectures. We will also see details how classical statistical concepts including maximum likelihood estimation, scaling laws, calibration, and preference optimization empower modern training pipelines. As a primary case study, we go through rigorous mathematical analysis of statistical text watermarking, focusing on green/red list generation, logit biasing, z-statistic hypothesis testing, detection power, and robustness against editing.

Commutative Algebra seminar
Speaker: Sayed Sadiqul Islam, IIT Bombay
Host: Tony Puthenpurakal
Title: Zariski Closedness of Supports of Local Cohomology Modules
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, September 30
Venue: Room No .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.

Mathematics Colloquium
Speaker: Hemanshu Kaul, Illinois Institute of Technology
Host: Niranjan Balachandran
Title: Counting Colorings: Variations and Extensions of a theme of Kostochka and Sidorenko
Time, day and date: 4:45:00 PM - 5:45:00 PM, Wednesday, September 30
Venue: Ramanujan Hall
Abstract: In 1990, Kostochka and Sidorenko introduced the List Color Function, which counts the guaranteed number of list colorings of a given graph, as a counterpart to the classic Chromatic Polynomial, introduced by Birkhoff in 1912, which counts its ordinary colorings. They asked whether the List Color Function asymptotically equals the Chromatic Polynomial when the number of colors is large enough. This was proved by Donner (1992) with several major improvements continuing to appear till now. This phenomenon has been widely studied in the context of generalizations of ordinary colorings.
In this talk, we will discuss the history as well as some new results on this theme of Kostochka and Sidorenko: an enumerative function of (a variant of) list colorings equals the corresponding enumerative function of (the same variant of) ordinary colorings, when the number of colors is large enough. We will also see when this phenomenon fails in context of DP-colorings but can still be recovered using the Tutte polynomial.