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: 11:30:00 AM - 12:30:00 PM, Monday, October 12
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: Parthe Pandit, IIT Bombay
Host: Parthanil Roy
Title: Precise Asymptotics of Statistical Linear Inverse Problems in High Dimensions
Time, day and date: 4:15:00 PM - 5:15:00 PM, Wednesday, October 14
Venue: Ramanujan Hall
Abstract: This is a tutorial-style talk on a class of algorithms studied under the name of Approximate Message Passing. These algorithms have a scalar State Evolution which enables characterizing the asymptotic behavior of their fixed points in a precise manner in the proportional high dimensional regime. This enables rigorous analysis of a large class of optimization formulations such as regularized M-estimation for generalized linear models, and structural risk minimization in machine learning.

Special Session
Speaker: Madhusudan Manjunath, IIT Bombay
Title: Mathematics for Well-Being (MW) IV: Math in the AI times cries for MW
Time, day and date: 10:30:00 AM - 11:30:00 AM, Thursday, October 15
Venue: Ramanujan Hall
Abstract: After a careful review of the current situation with AI involvement in Mathematics, we formulate key questions that arise in this context. We outline the guidance MW provides here. Special emphasis will be given to India's unique position to guide the community through this challenging time.

Geometry and Topology seminar
Speaker: Sumanta Das, IIT Bombay
Host: Rekha Santhanam
Title: Exotic Open Contractible 3-Manifolds and Asymptotic Limits
Time, day and date: 2:30:00 PM - 3:30:00 PM, Thursday, October 15
Venue: Ramanujan Hall
Abstract: In 1934, Whitehead proposed a proof of the Poincaré conjecture. It rested on the claim that every open contractible 3-manifold is homeomorphic to Euclidean 3-space. The following year he found the claim to be false. He then published a counterexample, now known as the Whitehead manifold. McMillan later produced uncountably many such manifolds, no two of them homeomorphic.

Telling Euclidean space apart from these exotic manifolds is delicate: they are contractible, so no ordinary homotopy invariant distinguishes them, and the whole of the difference sits at infinity, where they are wild. The invariant that does see it is the Brown-Grossman proper fundamental group, extracted from an inverse sequence of ordinary fundamental groups by a tool developed by Brown. We call this tool the asymptotic limit functor.

In this talk, we will explain the construction, and show that the asymptotic limit behaves considerably better than the inverse limit and its first derived functor. We will then use it to quantify the wildness algebraically: every open contractible 3-manifold not homeomorphic to Euclidean 3-space has exactly one end, and its Brown-Grossman proper fundamental group is uncountable and perfect. This contrasts sharply with the ordinary fundamental group of a manifold, which is always countable.

Joint work with Rekha Santhanam. Based on arXiv:2609.14063.

Algebraic Groups Seminar
Speaker: Shripad M. Garge, IIT Bombay
Title: -
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, October 15
Venue: Room 215
Abstract: Brief review of chapter 8, a review of chapter 9, and possibly the first section of chapter 10. 

Students' Seminar
Speaker: Harshita Agarwal, IIT Bombay
Host: Suman Kumar Sahoo
Title: Physics-Informed Neural Networks: A mathematical Introduction|
Time, day and date: 4:00:00 PM – 5:00:00 PM, Friday, October 16
Venue: Ramanujan Hall (https://meet.google.com/aon-mshf-ovk)
Abstract: Neural networks are usually trained using only examples. But often we also know a simple mathematical rule the answer should follow — even when we don't have much data to work with. This talk introduces Physics-Informed Neural Networks (PINNs): a simple way to teach a network to respect such a rule, using nothing more than ideas we already know — the chain rule and gradient descent. We'll build the idea step by step, from how a basic network learns, to how it can check a rule exactly, and finally see it all come together on one simple example. No physics or PDE background is needed; the talk stays friendly and non-technical throughout, explained through pictures and one running example rather than long derivations.