13:15 - 14:15 Lynn Chua (UC Berkeley), 14:30 - 15:30 Francesco Galuppi (MPI Leipzig)
Wednesday, February 13, 2019 - 13:15
HU, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, 3.011, Erdgeschoss
Forschungsseminar "Algebraische Geometrie"
Prof. Dr. Gavril Farkas, Prof. Dr. Bruno Klingler
Chua: We present a new perspective on the Schottky problem that links numerical computing with tropical geometry. The task is to decide whether a symmetric matrix defines a Jacobian, and, if so, to compute the curve and its canonical embedding. We offer solutions and their implementations in genus four, both classically and tropically. The locus of cographic matroids arises from tropicalizing the Schottky-Igusa modular form. This is joint work with Mario Kummer and Bernd Sturmfels. Galuppi: Signature tensors are a useful tool in the study of paths X. When X runs among a given class of path (e.g. polynomial, piecewise linear, etc), the signature of X parametrizes an algebraic variety. The geometry of this variety reflects some of the properties of the chosen class of path. The most important example is the class of rough paths, that are widely studied in stochastic analysis. Their signature variety presents many similarities to the Veronese variety, and we'll illustrate the first nice results, as well as some open questions.
submitted by Kristina Schulze (schulze@math.hu-berlin.de)