Graduiertenkolleg: Methods for Discrete Structures

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Monday Lecture and Colloquium

Monday, December 5, 2016

Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
room MA 041

Lecture - 14:15

Antonio Lerario - SISSA, Triest

Probabilistic enumerative geometry

Classical enumerative geometry deals with questions like: “How many lines intersect four lines in general position in three-dimensional space?” The answer to this type of questions is provided by a beautiful, sophisticated machinery, which goes under the name of Schubert calculus. Over the real numbers this classical approach fails—there is no generic number of real solutions, which can already be seen in the basic problem of counting the real solutions to a polynomial equation. Understanding even the possible outcomes for higher dimensional versions of the problem becomes increasingly complicated. In this talk I will discuss how enumerative problems over the reals can be studied in a probabilistic way, by answering questions like: “On average, how many real lines intersect four random lines in three-dimensional space?”.
(This is joint work with P. Bürgisser)

Colloquium - 16:00

Paul Breiding - Technische Universität Berlin

The condition number of join decomposition

Joins of real manifolds appear in a wide area of application and often one is interested in decomposing a point on a join into its factors. Naturally, one may expect that the performance of any numerical algorithm that solves the join decomposition problem is governed by the condition number of the problem. In this talk I will define the condition number of the join decomposition problem and describe it as the inverse distance to some ill-posed set in a product of Grassmannians. Moreover, I will model the join decomposition as an optimization problem, provide an algorithm for it and explain how the condition number influences the performance of this algorithm. Finally, I will show you the behaviour of the condition number close to boundary points of the join.
This is joint work with Nick Vannieuwenhoven.

Letzte Aktualisierung: 29.11.2016