Organizer: Analysis group at IITB
Email: cbiswas (AT) iitb.ac.in
Time: Mondays, 4pm - 5pm
Room: Ramanujan Hall, Department of mathematics, IITB
All talks will be in-person unless otherwise specified. If necessary the seminar might be scheduled at a different time to accommodate speakers.
Date and Time: Monday 6 Nov, 2023, 5:30 - 6:30 pm
Venue: Ramanujan Hall, Zoom talk online
Speaker: Ayush Khaitan
Affiliation: Rutgurs University
Title: Conformal Geometry and Ricci flow
Abstract: We study a surprising duality between conformal geometry and Ricci flow. Using a classical construction called the Fefferman-Graham ambient space, we construct an infinite family of fully nonlinear analogues of Perelman's F and W functionals, and study their monotonicity under several natural conditions.
Date and Time: Monday 13 Nov, 2023, 4pm - 5pm
Venue: Ramanujan Hall
Speaker: Senthil Raani
Affiliation: IISER Berhampore
Title: Distance Set Problems
Abstract: The distance set ∆(E) of a set E in Euclidean space consists of all non-negative numbers that represent distances between pairs of points in E. How does the structure of E impact that of ∆(E)? Questions of this nature play a fundamental role in geometric measure theory. We will begin with a brief history of results and conjectures on ∆(E). Apart from measure theoretic techniques, the asymptotic of the Fourier transform of measures supported on E plays a vital role in this study. Our main goal in this talk is to discuss a few properties of ∆(E) when E is sparse but has a large Hausdorff dimension. This is based on recent joint work with Prof. Malabika Pramanik.
Date and Time: Monday 20 Nov, 2023, 4pm - 5pm
Venue: Ramanujan Hall
Speaker: Ankit Bhojak
Affiliation: IISER Bhopal
Title: Sharp endpoint $L^p-$estimates for bilinear spherical maximal functions
Abstract: Abstract
Date and Time: Monday 4 Dec, 2023, 1:30pm - 2:30 pm
Venue: Zoom talk online,
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 pure point with polynomial eigenfields. I will give a conceptual proof of this fact and an asymptotic result on the eigenvalues.