Donnerstag, 15.12.2022, 17:00-18:00; G02-210
Im Rahmen des Mathematischen Kolloquiums trägt
Herr Prof. Serkan Hosten
San Francisco State University
''Gram spectrahedra of binary vs. symmetric binary forms''
Real polynomials that are sum-of-squares (SOS) have been studied for over 150 years and they have made a
significant comeback in the context of polynomial optimization. Given an SOS polynomial, all possible SOS representations
of this polynomial are parametrized by the points of a convex set called the Gram spectrahedron of the polynomial.
I will report on the geometric and combinatorial structure of Gram spectrahedra of binary and symmetric binary forms.
In particular, I will present a characterization of extreme points of these spectrahedra for symmetric binary forms that are of rank two.
This is complementary to a classical result in the non-symmetric case. I will also report what we know about the facial structure and
combinatorics of the same spectrahedra.
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