Geometry Seminar / Graduate Lectures

Polynomial interpolation in Riemannian manifolds and Lie groups
 

Dimitrii Pavlov (MPI Leipzig)
Combinatorics of m=1 Grasstopes

Abstract: A Grasstope is the image of the totally nonnegative Grassmannian $\mathrm{Gr}_{\geq 0}(k,n)$ under a linear map $\mathrm{Gr}(k,n)\dashrightarrow \mathrm{Gr}(k,k+m)$. This is a generalization of the amplituhedron, a geometric object of great importance to calculating scattering amplitudes in physics. The amplituhedron is a Grasstope arising from a totally positive linear map. While amplituhedra are relatively well-studied, much less is known about general Grasstopes. In this talk, I will discuss combinatorics and geometry of Grasstopes in the m=1 case. In particular, I will show that they can be characterized as unions of cells of a hyperplane arrangement satisfying a certain sign variation condition. This is based on joint work with Yelena Mandelshtam and Lizzie Pratt.

Mario Kummer (TU Dresden)
Fourier Quasicrystals
 

Max Schmidt (TU Dresden)
Master Thesis Defence:
Amenability for unitary groups of C*-algebras

Geometry Seminar
David Sawall (Universität Konstanz)
Amalgamation of Real Zero Polynomials

Abstract: Whenever a polynomial arises form another polynomial by substituting zero for some variables, we call the second polynomial an extension of the first one. A real multivariate polynomial is called real zero if it has only real zeros along all lines through the origin. In the main part of this talk, we will show that there are real zero polynomials which do not have a common extension (called amalgam) which is again real zero. Additionally, I will state some cases where real zero amalgams exist and discuss some open problems. (Joint work with Markus Schweighofer.)

Tentative Schedule:
Sept 20^th, 9:30 – 11:00  (Wednesday)
Sept 22^th, 9:30 – 11:00  (Friday)
Sept 25^th, 9:30 – 11:00  (Monday)
Sept 26^th, 9:30 – 11:00  (Tuesday)
Information, Abstract, Registration, Participation via Zoom
Contact: Prof. Dr. St. Neukamm