Geometric Structures - Clayton Shonkwiler - Feb 23 - 4:15 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All, 

This is a reminder of today's seminar from the series "Geometric
Structures".

Speaker: CLAYTON SHONKWILER [1] (Colorado State University) [1] 

Title: The (Symplectic) Geometry of Spaces of Frames 

Time: February 23, 2021, 4:15 pm (Rome Time)  

Venue: from remote only, on zoom at this link 
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[2]
Passcode: geometry

Abstract:  

A frame for a finite-dimensional complex vector space is simply a
spanning set. Frames include bases, but also spanning sets that are
larger than a basis, and hence more suitable for applications where
robustness to noise and erasures are important. In applications, frames
are sometimes also called overcomplete dictionaries. 

In applications we typically want to impose some structure on our frame,
for example by requiring each frame vector to be unit-length or by
requiring that the frame satisfies the Parseval identity. While frames
satisfying these and similar constraints form (real) algebraic
varieties, it can be challenging to extract useful information from this
perspective. 

My goal in this talk is to introduce a symplectic perspective on frames,
and in particular to describe how many of the constraints on frames
which are used in applications arise quite naturally in symplectic
geometry, giving new insight into some important problems in frame
theory, including the frame homotopy conjecture and the genericity of
full spark frames. This is joint work with Tom Needham. 

More information can be found here:
https://sites.google.com/view/geometric-structures/ [3] 

Everyone is welcome! 
-- 
_Miruna-Stefana Sorea_
_Postdoctoral Researcher_
_Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste,
Italy_
_HTTPS://SITES.GOOGLE.COM/VIEW/MIRUNASTEFANASOREA/_ 

Links:
------
[1]
https://www.google.com/url?q=https%3A%2F%2Fwww.math.colostate.edu%2F~clayton%2F&sa=D&sntz=1&usg=AFQjCNHx-Q3cMy2Xq52OA0eeyr0MV0BJIw
[2]
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[3] https://sites.google.com/view/geometric-structures/