Abstracts FU Berlin - November 2017

Please also see the programm of the seminar.

Carlos Amendola (TU Berlin)
Discrete Gaussian Distributions Via Theta Functions

Maximum entropy probability distributions are important for information theory and relate directly to exponential families in statistics. Having the property of maximizing entropy can be used to define a discrete analogue of the classical continuous Gaussian distribution. We present a parametrization of such a density using the Riemann Theta function, use it to derive fundamental properties which include computing its characteristic function, and exhibit connections to the study of abelian varieties. This is joint work with Daniele Agostini (HU Berlin).

June Huh (IAS Princeton)
Negative correlation and Hodge-Riemann relations

All finite graphs satisfy the two properties mentioned in the title. I will explain what I mean by this, and speculate on generalizations and interconnections. This talk will be non-technical: Nothing will be assumed beyond basic linear algebra.

Kathlen Kohn (TU Berlin)
Isotropic Subvarieties of Grassmannians

I will present very recent results obtained together with James Mathews during his stay at TU Berlin and MPI MIS Leipzig. We will discuss the notion of isotropic varieties, with a focus on isotropic curves, congruences and fully-isotropic varieties. The talk will concentrate on examples and our general techniques.

Şevda Kurul (Johann Wolfgang Goethe-Universität Frankfurt/M)
On the birational geometry of arrangement complements

The complement of a hyperplane arrangement in the projective space can be naturally identified with a subvariety of its intrinsic torus. Tevelev shows that for certain toric varieties one gets nice compactifications by taking the closure of the arrangement complement in these toric varieties (tropical compactifications). In this talk we give an introduction to tropical compactifications and show that automorphisms of a large class of arrangement complements can be extended to automorphisms of their visible contour compactification, a special case of tropical compactification.

Sandra di Rocco (KTH Stockholm)
Interactions between algebraic geometry and Kinematics

Effective models of various kinematics problems rely on algebraic geometry. The theory of projective varieties, intersection theory and group actions are helpful tools for the construction of numerical algorithms. I will illustrate these (by now) classical algebraic models and their role in solving (inverse) kinematics problems. Inverse Kinematics problems admitting a higher dimensional variety as solutions have not been much explored. I will briefly explain how certain sampling techniques can be effective in understanding the topology of such varieties.

Benjamin Schröter (TU Berlin)
Multi-splits and Matroids

Multi-splits are a class of coarsest regular subdivisions of convex polytopes. In this talk I will present a characterization of all multi-splits of two types of polytopes, namely products of simplices and hypersimplices. It turns out that the multi-splits of these polytopes are in correspondence with one another. Moreover, matroid theory is the key in their analysis, as all cells in a multi-split of a hypersimplex are matroid polytopes.

Akiyoshi Tsuchiya (Osaka University)
Normality and levelness of Cayley sums

Normality or the integer decomposition property (IDP) is one of the most important properties on lattice polytopes. In fact, many authors have been studied the properties from view-points of combinatorics, commutative algebra and algebraic geometry. In this talk, we discuss when a Cayley sum is IDP. Moreover, we consider when a Cayley sum is level.