CMIT | Tangent Tuesdays, 3rd September 2024 | 4pm

Speaker: Arjun V Nair (B20 Math major, Interned at Ecole Polytechnique, Paris)
Title: Some secrets of the Helmholtz equation (Part 2)
Date and Time: 3rd September 2024 | 4pm
Venue: PSB 1104

Abstract: As my summer began, I studied/revised concepts or fundamentals in related areas of Mathematics (Analysis, Inverse Problems, PDEs, etc...). Then I had to decide what open problem I may begin reading further. In the field of Inverse problems, holographic uniqueness problems for various PDEs are important, quite often for Physics. This class of problems was studied well and resolved for the three-dimensional and one-dimensional Helmholtz equation. The two-dimensional setting was seemingly complicated and hence made for an ideal reading project. However, during the course of the internship, I was able to find some mathematical techniques through which we were able to resolve this open problem. We will be publishing two papers in connection to this work and some further implications. In this talk, I intend to discuss the first of these papers and the adventure of this research experience. Refer here for the abstract. The second one may be discussed on some other occasion. “Arxiv themes - Analysis of PDEs, Mathematical Physics”.