Title: A positive dichotomy between Diophantine geometry and Dynkin friezes

Abstract: General finiteness results for positive integer solutions to Diophantine equations are rare. In this talk, I will describe how the theory of cluster algebras can be a remarkable source of finiteness & infinitude in the form of a Siegel theorem for positive integral points on affine varieties. On the finiteness of positive integral points, I will highlight 7-dimensional and 8-dimensional affine varieties that arise in the Fontaine–Plamondon conjecture on Dynkin friezes. On the infinitude of positive integral points, I will highlight surfaces and threefolds that arise in the Mordell–Schinzel program on Diophantine equations xyz = G(x, y).

Prof Amod Agashe, Florida State University with title and abstract as below.

Title: The zeros of the Riemann zeta function and its generalization to modular forms

Abstract: The Riemann hypothesis, one of the most important open problems in mathematics, says that the Riemann zeta function should have zeros only at complex numbers with real part ⁠1/2 and at negative even integers. We will study the completed Riemann zeta function (the one with the Gamma factor) and discuss how it sheds some light on the location of the zeros. There is a generalization of the Riemann hypothesis to L-functions of modular forms, and we will discuss what can be said in this context. The talk should be accessible to advanced undergraduates and graduate students, including those in engineering.
 

Speaker: Dr Kaustubh Mondal: IISER Pune

Title : A Finite Linear Dependence of Discrete Series Multiplicities

Abstract : Let $G$ be a non-compact connected semisimple Lie group with a compact Cartan subgroup and $\Gamma$ be a uniform lattice in $G$. In this talk, we will describe that an infinite set of discrete series multiplicities in $L^2(\Gamma \backslash G)$ can be determined from any finite subset satisfying a certain condition. This result leads to a refinement of the strong multiplicity one theorem for discrete series representations. We will conclude the talk by illustrating an application of this result in the context of spaces of holomorphic cusp forms. This is a joint work with Gunja Sachdeva. 

Number theory seminar
Speaker: Dr. Bibekananda Maji (IIT Indore)
Host: Kummari Mallesham
Title: A number field analogue of Ramanujan's formula for zeta(2m+1)
Time, day and date: 10:00:00 AM, Monday, June 23
Venue: Ramanujan Hall
Abstract: Ramanujan's famous formula for odd zeta values has been studied by many mathematicians over the years. In 1972, Grosswald found a simple extension of Ramanujan's formula which in turn gives a transformation formula for the Eisenstein series. In this talk, we will discuss a new number field analogue of the Ramanujan-Grosswald formula for zeta(2m+1) by obtaining a formula for the Dedekind zeta function at odd arguments. This is joint work with Diksha Rani Bansal.

Algebraic geometry seminar
Speaker: Snehajit Misra (IIT-ISM Dhanbad)
Host: Sudarshan Gurjar
Title: Some results on Seshadri constants of vector bundles
Time, day and date: 4:00:00 PM, Tuesday, June 24
Venue: Ramanujan Hall
Abstract: Seshadri constants of nef line bundles on smooth complex projective varieties were introduced by J.P. Demailly to tackle Fujita conjecture. Later on, these constants were defined by C. Hacon for nef vector bundles, and subsequently studied by Fulger-Murayama for relatively nef line bundles in a relative setting. In this talk, we will survey the known results in literature about Seshadri constants for vector bundles and will discuss our recent results on Lazarsfeld-Ein type inequality satisfied by these constants. This talk is based on joint work with Indranil Biswas and Krishna Hanumanthu.

Thesis Defence seminar
Speaker: Mr. Niphadkar Shubham Sanjay (IIT Bombay)
Host: Siuli Mukhopadhyay
Title: Design considerations for crossover trials with multiple responses
Time, day and date: 10:00:00 AM, Wednesday, June 25
Venue: Ramanujan Hall
Abstract: -

Professor Ila Varma from University of Toronto will give a colloquium in the
Ramanujan Hall at 4 pm, on Wednesday 25th June.

Title: Counting number fields and predicting asymptotics

Abstract: A guiding question in number theory, specifically in arithmetic statistics, is: Fix a degree n and a Galois group G in S_n. How does the count of number fields of degree n whose normal closure has Galois group G grow as their discriminants tend to infinity? In this talk, we will discuss the history of this question and take a closer look at the story in the case that $n = 4$, i.e. the counts of quartic fields.
 

Speaker: Shuvayan Banerjee (IIT Bombay)
Host: Radhendushka Srivastava
Title: Pre synopsis seminar
Time, day and date: 7:00:00 AM, Thursday, June 26
Venue: Online (https://meet.google.com/bby-rcae-wvz)
Abstract: This talk addresses the challenges of bias and model mismatch in sparse signal estimation, particularly within compressed sensing (CS)-based group testing frameworks. It is structured in three parts. First, we present a novel, closed-form solution for efficiently computing the debiasing matrix W for the LASSO estimator by reparameterizing the optimization problem originally posed by Javanmard and Montanari(2014). This approach preserves theoretical guarantees while avoiding the computational burden of estimating the debiasing matrix. In the second part, we introduce theOptimal Debiased Robust Lasso Test Method (ODrlt), a testing framework for identifying model mismatch errors (MMEs) in group testing, which integrates debiased estimation with dual hypothesis testing to detect defective samples and mis-specified groups. We provide theoretical error bounds and demonstrate superior performance over baseline methods. The final part of the thesis develops two correction algorithms—one based on the ODrlt test statistic and the other on LASSO goodness of fit—which operate within a multi-stage correction scheme guided by potential functions to iteratively refine group membership and correct MMEs.