Geometric Structures - Kathlén Kohn - Jan 19 - 4:00 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All, 

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

Speaker: KATHLÉN KOHN [1] ( [2]KTH Royal Institute of Technology [2],
[2] Stockholm [2]) [2] 

Title: The adjoint of a polytope

Time: January 19, 2021, 4:00 pm (Rome Time) 

Venue: from remote only, on zoom at this link 
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[3]
Passcode: geometry

Abstract: This talk brings many areas together: discrete geometry,
statistics, intersection theory, classical algebraic geometry, geometric
modeling, and physics. First, we recall the definition of the adjoint of
a polytope given by Warren in 1996 in the context of geometric modeling.
He defined this polynomial to generalize barycentric coordinates from
simplices to arbitrary polytopes. Secondly, we show how this polynomial
appears in statistics. It is the numerator of a generating function over
all moments of the uniform probability distribution on a polytope.
Thirdly, we prove the conjecture that the adjoint is the unique
polynomial of minimal degree which vanishes on the non-faces of a simple
polytope. In addition, we see that the adjoint appears as the central
piece in Segre classes of monomial schemes, and in the study of
scattering amplitudes in particle physics. Finally, we observe that
adjoints of polytopes are special cases of the classical notion of
adjoints of divisors. Since the adjoint of a simple polytope is unique,
the corresponding divisors have unique canonical curves. In the case of
three-dimensional polytopes, we show that these divisors are either K3 -
or elliptic surfaces. 

This talk is based on joint works with Kristian Ranestad, Boris Shapiro
and Bernd Sturmfels. 

  More information can be found here:
https://sites.google.com/view/geometric-structures/ [4] 

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://kathlenkohn.github.io/
[2]
https://www.google.com/url?q=https%3A%2F%2Fkathlenkohn.github.io%2F&sa=D&sntz=1&usg=AFQjCNHYRqTkv2LOC6U_BeBOkPeMbHW_2A
[3]
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[4] https://sites.google.com/view/geometric-structures/