Geometric Structures seminar - Paul Breiding - June 9, 2022 - 2:00 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All,

This is to announce the next seminar from the series "Geometric Structures".

Speaker: Paul Breiding<https://pbrdng.github.io/index.html> (Max Planck Institute for Mathematics in the Sciences, Leipzig)

Title: Facet Volumes of Polytopes

Time: June 9, 2022, 2:00 pm (Rome Time)
Venue: room 134
on zoom at this link:
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry

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Abstract:
We consider what we call facet volume vectors of polytopes. Every full-dimensional polytope in R^d with n facets defines n positive real numbers: the n (d-1)-dimensional volumes of its facets. For instance, every triangle defines three lenghts; every tetrahedron defines four areas.
We study the space of all such vectors. We show that for fixed integers d\geq 2 and n\geq d+1 the configuration space of all facet volume vectors of all d-polytopes in R^d with n facets is a full dimensional cone in R^n, and we describe this cone in terms of inequalities. For tetrahedra this is a cone over a regular octahedron.
Joint work with Pavle Blagojevic and Alexander Heaton.

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More information can be found here: https://sites.google.com/view/geometric-structures/
Everyone is welcome!


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Miruna-Stefana Sorea
Postdoctoral Researcher
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
https://sites.google.com/view/mirunastefanasorea/