Tbilisi Analysis & PDE Seminar


Tbilisi Analysis & PDE Seminar

Dear Colleagues! 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 Mondays at 20:00 local time in Tbilisi (compare to your local time https://www.timeanddate.com/worldclock/georgia/tbilisi).

Seminar on January 23, 2024

Speaker: Prof. em. Elias Wegert, Institute of Applied Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany; https://de.wikipedia.org/wiki/Elias_Wegert

The title of the lecture: “Numerical Range, Blaschke Products, and Poncelet Polygons”

Abstract: In 2016, Gau, Wang and Wu conjectured that a partial isometry \( A \) acting on a \( n \)-dimensional complex Hilbert space cannot have a circular numerical range with a non-zero centre. In this talk, we verify this for operators with \( \mathrm{rank}\,A = n - 1 \).

The proof is based on the unitary similarity of \( A \) to a compressed shift operator generated by a finite Blaschke product \( B \). We then use the description of the numerical range by Poncelet polygons associated with \( B \), a special representation of Blaschke products related to boundary interpolation, and an explicit formula for the barycenters of the vertices of Poncelet polygons involving elliptic functions.

The talk is a mixture of operator theory, plain geometry, and elementary complex analysis. In particular, we give a short introduction to the visualization of complex functions by „phase plots“ and demonstrate how they can help to discover relevant properties of these functions.

Full abstract see here: https://drive.google.com/file/d/1u44q9liZP6IxAwECBwRS7Lpkq9hmoSIz/view?usp=sharing

Download poster: Link to Download

How to join: The seminar is organized on the Cisco Webex Meetings. 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.

Join information  
Meeting link: https://ug.webex.com/ug/j.php?MTID=m3e771123c33401dc28ca7c54fb64efd1  
Meeting number: 2400 904 2245  
Password: W8zMmrpVS84 (98966778 from phones and video systems)  

 

 

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






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STAY INFORMED
Stay connected and get the latest information
SUBSCRIBE
OUR SOCIAL NETWORKS
UG
CONTACT
Address: 77a, M. Kostava str. Tbilisi, 0171, Georgia Tel: 2 55 22 22; info@ug.edu.ge
ADDITIONAL LINKS
All Rights Reserved. Copyright © 2018 The University of Georgia