Tbilisi Analysis & PDE Seminar

Tbilisi Analysis & PDE Seminar

Dear Colleagues! V. Kupradze Institute of Mathematics of the University of Georgia is pleased to invite you to the Online Tbilisi Analysis & PDE Seminar. The seminar is held bi-weekly on Tuesdays at 20:00 local time in Tbilisi (compare to your local time https://www.timeanddate.com/worldclock/georgia/tbilisi).

Seminar on March 4, 2025

Speaker: Dr. Ryan O’Loughlin, University of Reading; https://www.ryanoloughlin.co.uk/

The title of the lecture: „Numerical Ranges and Crouzeix's Conjecture“

Abstract: The numerical range of a matrix is a convex compact subset of the complex plane. This is a fundamental concept in linear algebra and finds uses in numerical analysis through the approximation of eigenvalues and in functional analysis via Crouzeix's Conjecture. In this talk, I will give a brief introduction to the numerical range of a matrix and present a new proof that the numerical range of a \( 2 \)-by-\( 2 \) matrix is an ellipse. I will then give a background on Crouzeix's Conjecture, which is an open conjecture which bounds the norm of a polynomial applied to a matrix by a constant multiplied by the supremum of the polynomial over the numerical range of the matrix. Finally, I will present new recently published results studying the continuity of the constant appearing in Crouzeix's Conjecture.

Download Poster: Link to Download

How to join: The seminar is organized on the Zoom Workplace. If you are already registered, you don't need to register again. Otherwise, to join the seminar please send an e-mail to seminarim@ug.edu.ge or register here:

https://forms.gle/xfQJ9fg1uqe7CrZw6

You will then receive further information.

You can also join an online seminar without installing Webex, by just clicking on the meeting link of the seminar. You will be connected via browser e.g. Firefox, Google Chrome, Microsoft Edge or whatever.

Past Seminars here

Organizers:

1. R. Duduchava, Institute of Mathematics, University of Georgia, Tbilisi
2. E. Shargorodsky, Department of Mathematics, King’s College London
3. G. Tephnadze, Institute of Mathematics, University of Georgia, Tbilisi

Secretary:

M. Tsaava, Institute of Mathematics, University of Georgia, Tbilisi
Technical support:

G. Tutberidze, Institute of Mathematics, University of Georgia, Tbilisi

Z. Vashakidze, Institute of Mathematics, University of Georgia, Tbilisi

Seminar of our partners:

Seminar on Analysis, Differential Equations and Mathematical Physics