Today: Geometric Structures seminar - Andrea Rosana - Tuesday March 5th, 2024 , 10:00 (Rome time) - room 136 at SISSA (and online)

[Samuel Borza]

Dear All,

This is to remind you of today's seminar from the series "Geometric Structures".

Speaker: Andrea Rosana (SISSA)

Title: The Grassmann Distance Degree
Time: Tuesday March 5th, 2024 , 10:00 (Rome time)
Venue: room 136 - SISSA main building and online
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Meeting ID: 856 7559 1787
Password: geometry

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Abstract:
Given a space endowed with a distance, how can we optimize the distance from a point to a given subset? In this talk we will explore two different settings for this problem. We will first focus on the classical Euclidean space were the subset will be given by an algebraic variety, leading to the notion of Euclidean Distance Degree (EDD). Then we will try to mimic this construction for Grassmannians when the subset is a subvariety. After explaining why the techniques used in the previous case fail, we will be able to define an analogue of the EDD, which we call Grassmann Distance Degree. In the last part we will focus on the case where the subvariety is a simple Schubert variety, finding an interesting connection between the geometry of the problem and Eckart-Young theorem.
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More information can be found here: https://sites.google.com/view/geometric-structures/

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Samuël Borza