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.