Geometric Structures - Martin Lotz - March 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: MARTIN LOTZ  [1](Warwick University) [1] 

Title: Concentration of Measure in Integral Geometry 

Time: March 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:  
Intrinsic volumes are fundamental geometric invariants that include the
Euler characteristic and the volume. Important results in integral
geometry relate the intrinsic volumes of random projections,
intersections, and sums of convex bodies to those of the individual
volumes. We present a new interpretations of classic results, based on
the observation that intrinsic volumes (both in spherical and Euclidean
settings) concentrate around certain indices. One consequence is, for
example, that as the dimension of a subspace varies, the average
intrinsic volume polynomial of a random projection of a convex body to
this subspace is as large as possible or is negligible, and the exact
location of the transition between these two cases can be expressed in
terms of a summary parameter associated with the convex body. Similar
phase transitions appear in related problems, including the rotation
mean formula, the slicing (Crofton) formula, and the kinematic formula.
This is joint work with Joel Tropp. 

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/ [4]_ 

Links:
------
[1]
http://www.google.com/url?q=http%3A%2F%2Fhomepages.warwick.ac.uk%2Fstaff%2FMartin.Lotz%2F&sa=D&sntz=1&usg=AFQjCNHDWH0j2cO0oNZP6bfTAk8bSifD2w
[2]
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[3] https://sites.google.com/view/geometric-structures/
[4] https://sites.google.com/view/mirunastefanasorea/