Special Lectures 2024

Table of Contents

Spring 2024

SL2402: Some elementary questions on tilings and homomorphisms and some non-elementary answers #

Speaker: Prof. Nishant Chandgotia (TIFR-CAM, Bangalore)
Abstract: We will talk about tilings of \(\mathbb{Z}^d\) by rectangles and see how non-trivial questions in algebra and analysis appear out of nowhere while we try to answer them.
References: [TBU]
Date and Time: Saturday, 2nd March 2024, 3:00 PM - 5:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Prof. Apoorva Khare (IISc, Bangalore)
Abstract: Given a finite metric space, when is it flat (i.e., embeds in a Euclidean space)? When is it spherical? What is the mathematics behind GPS? As we will prove in the talk, the answers to all of these questions involve only one idea: Gram matrices. Like Bond and Bourne, these too have numerous aliases: covariance matrices, positive semidefinite matrices, and modified Cayley-Menger matrices. After discussing these aliases and questions, we end with another application: the 2000-year-old formula of Heron, and its generalization to \(2024\)-dimensional triangles (or \(n\)-dimensional simplices).
References: (See the notes)
Notes: Available here.
Video: Available here.
Date and Time: Monday, 22nd January 2024, 5:00 PM - 7:00 PM
Venue: 2nd Floor Auditorium, Academic Building