Postgraduate Seminars

These seminars (unless otherwise stated) will take place on Tuesdays at 12pm-1pm on an almost weekly basis.

Summer 2024

Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students.

25 April 2024 in 25 Gordon Street - Room 416 - 2pm-3pm

Speaker: Alexey Derkach

TITLE: some tools for spectral analysis of compact operators on hilbert space 

Abstract:   
Studying the asymptotics of eigenvalues is a classic question in Spectral theory. For a compact operator on a Hilbert space we usually estimate the decay of the s-numbers (singular values). In this talk I will discuss the connection between eigenvalues and s-values, the p-Schatten norms (and quasinorms), the Weidl operator classes and basic elements of Perturbation theory. We will see when it is easy to obtain an asymptotic formula and when we can give an asymptotic estimate only. These tools help to estimate the eigen/singular values of integral operators whose kernels satisfy certain conditions, (we will see how the rate of decay depends on the smoothness of the kernel). Mostly I am planning to discuss some general facts in this theory, but also want to mention the operators I study in my research, and the results obtained.

Zoom link: https://ucl.zoom.us/j/99473974347