Mathematics Seminars and Colloquia

4 December 2023- 9 December 2023

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Lecture series on algebraic stacks

Monday, 4th December, 11:30 am

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Host: Sudarshan Gurjar

Venue: Ramanujan Hall

Speaker: Nitin Nitsure, TIFR (retd)

Title: Gerbes and their cohomology classes

Abstract: Locally trivial fiber bundles can be described by their transition functions, giving a class in the first Cech cohomology of the structure group. Gerbes can be regarded as a `higher' version of this twisting phenomenon. The local description of a gerbe gives rise to a class in the second Cech cohomology of the base with coefficients in the `band' (lien in French) of the gerbe. This description of the cohomology class of a gerbe is particularly simple when the band is abelian, which is the case we will describe in this talk. The cohomological Brauer class of Azumaya algebra (or of a projective bundle) is an example of such a cohomological class.

Analysis seminar
Monday 4 Dec, 2023, 1:30 pm - 2:30 pm

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Venue: Meeting ID: 835 4823 3902, Passcode: 585182

Join Zoom Meeting

https://us06web.zoom.us/j/83548233902?pwd=A9bwLvfOJtpO88Dmzk1di4YaUq37aZ.1

Host: Chandan Biswas

Speaker: Yves Colin de Verdière

Affiliation: Fourier Institute, CNRS, University of Grenoble I

Title: On the spectrum of the Poincaré operator in ellipsoids.

Abstract: The Poincaré equation describes the motion of an incompressible fluid in a domain submitted to a rotation. The associated wave operator is called the "Poincaré operator". If the domain is an ellipsoid, it was observed by several physicists that the spectrum is a pure point with polynomial eigenfields. I will give conceptual proof of this fact and an asymptotic result on the eigenvalues.

Analysis seminar: An IPDF talk

Wednesday, December 6 at 10.30 am

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Venue: Meeting ID: 818 7750 5751, Passcode: 671479
https://us06web.zoom.us/j/81877505751?pwd=rqLYSbLv1bYxahPYpPa0cGMmNXEjPr.1
Host: Mayukh Mukherjee

Speaker: Ramesh Chandra Sau,

Affiliation: The Chinese University of Hong Kong 

Title: An Analysis and Solution of Optimal Control Problems: Classical to
Modern Approaches.

Abstract: In this talk, I will present both classical approaches (e.g., EFM) and modern approaches (using deep learning tools) to solve and analyze optimal control problems. The first part of this talk will be based on the energy space formulation of Dirichlet boundary control problems. We propose a finite element-based numerical method to solve the Dirichlet boundary control problem and derive error estimates in the energy norm. In the second part, we discuss solving optimal control problems using physics-informed neural networks (C-PINN). We describe $L^2(\Omega)$ error bounds in terms of neural network parameters and number of sampling points. We present some numerical examples to illustrate the approach (C-PINN) and compare it with existing approaches