Geometry and Topology seminar
Speaker: Pritthijit Biswas, IIT Bombay
Host: Rekha Santhanam
Title: Brill-Noether loci inside the moduli space of stable vector bundles over curves
Time, day and date: 11:30:00 AM - 12:30:00 PM, Thursday, October 16
Venue: Ramanujan Hall
Abstract: Let X be a smooth projective curve of genus g over the field C. Let M_{X}(2, L)denote the moduli space of stable rank 2 vector bundles on X with fixed determinant L of degree 2g-1. Consider the Brill-Noether subvariety W ^{1}_{X} (2, L) of M_{X} (2, L) which parametrises stable vector bundles having at least two linearly independent global sections. In this talk, for generic X and L, I would outline a proof of the fact that W ^{1}_{X} (2, L) is stably-rational when g = 3 and unirational when g = 4. This is a part of joint work with Jaya NN Iyer.

Student Seminar
Speaker: Saibur Alom, IIT Bombay
Host: Santanu Dey
Title: Fourier Transform of Hilbert Transform on R^n
Time, day and date: 2:00:00 PM – 2:45:00 PM, Thursday, October 16
Venue: Room 113

Student Seminar
Speaker: Subir Dakshi, IIT Bombay
Host: Santanu Dey
Title: The Hardy-Littlewood maximal function
Time, day and date: 2:45:00 PM – 3:30:00 PM, Thursday, October 16
Venue: Room 113

Commutative algebra seminar
Speaker: Prof. R. V. Gurjar
Date: 16 Oct 2025
Day Thursday
Venue: Ramanujam Hall
Time 4-5 pm
Title: Resolution of singularities of algebraic or analytic varieties.

Abstract.
First I will show how to resolve curve singularities (this must be
well-known to many). Then discuss Jung-Hirzebruch argument to get the
equation of a surface in three variables in a very simple form, and then
resolve its singularities. This will complete the proof of resolution of
singularitiies of surfaces. Next I will discuss some easy but useful
results about resolution type results (resolution of indeterminacies,
principalization, general notion of resolution of singularities, and their
relations to each other).

Statistics/Probability Seminar
Speaker: Mayukh Choudhury, IIT Bombay
Host: Debraj Das
Title: Asymptotic Theory of $K$-fold Cross-validation in Lasso and the Validity of Bootstrap
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, October 16
Venue: Ramanujan Hall (meet.google.com/bgr-tffn-cem)
Abstract: Lasso is one of the widely used regularization methods in regression. Statisticians usually implement Lasso in practice by choosing the penalty parameter in a data-dependent way, the most popular being the $K-$fold cross-validation (or $K-$fold CV). However, inferential properties, such as the variable selection consistency and $n^{1/2}-$consistency, of the $K-$fold CV based Lasso estimator and validity of the Bootstrap approximation are still unknown. In this talk, we will discuss about $n^{1/2}-$consistency of the $K$-fold CV based penalty and utilizing that we explore the aforementioned inferential properties of the underlying Lasso estimator. Additionally, we establish the validity of Bootstrap in approximating the distribution of the $K-$fold CV based Lasso estimator. We validate our Bootstrap method in finite samples based on simulations.