Vorträge in der Woche 08.05.2023 bis 14.05.2023

Montag, 08.05.2023: Vortrag in der Reihe "Mathematiker im Beruf" - Was haben Wahlkreise und Vertriebsgebiete miteinander zu tun? - Gestalten Sie mit Mathematik!

Dr. Hans Georg Freiermuth (Sparkassen Pensionskasse AG, Sparkassen Pensionsfonds AG - Sprecher des Vorstands; Sparkassen PensionsManagment GmbH - Sprecher der Geschäftsführung)

In der Vortragsreihe "Mathematiker im Beruf", die sich vor allem an die Studierenden des Fachbereichs Mathematik richtet, berichten Mathematiker über ihren Werdegang, ihr jetziges Arbeitsfeld und wie ihnen ihr Mathematikstudium dabei zu gute kommt. -- Zur Entscheidungsfindung in Unternehmen spielen mitunter auch mathematische Methoden eine wichtige Rolle. Anhand eines Beispiels aus dem Vertrieb skizziert der Vortragende, wie Sie als Mathematikerin oder Mathematiker mit Wissen, strukturiertem Denken und Kreativität in der Lebensversicherungswirtschaft mitgestalten können. Wenn die Zeit es erlaubt, erzählt er zudem ein wenig über seine Metamorphose vom Algebraischen Geometer zum Manager - und was hierbei rückblickend in den letzten 15 Jahren Hürden und Erfolgsfaktoren waren.

Dienstag, 09.05.2023: LCA groups

Hannah Markwig

Mittwoch, 10.05.2023: An Algorithm to Compute Plane Tropical Curves with "tropical.lib"

Levin Stuke (Tübingen)

I will present an algorithm that computes plane tropical curves from their defining polynomials. This algorithm is implemented in the "tropical.lib" library in the computer algebra system Singular. It can be used to draw plane tropical curves and their dual Newton Subdivisions. I will review some basics about plane tropical curves, explain the algorithm and show some hands-on examples with "tropical.lib". I will also present a new functionality of "tropical.lib" that broadens the class of possible input polynomials. The talk is based on work from my bachelor's thesis.

Mittwoch, 10.05.2023: Sharp bounds on fake weighted projective spaces

Andreas Bäuerle (Universität Tübingen)

Fake weighted projective spaces are the $\mathbb{Q}$-factorial toric Fano varieties of Picard number one. They form an interesting example class for the general question of bounding geometric data of a Fano variety in terms of its singularities. One invariant of the singularities is the Gorenstein index, ie. the smallest positive integer $g$ such that the $g$-fold of the anticanonical class is Cartier. We give a sharp upper bound on the anticanonical degree of a fake weighted projective space $X$ that only depends on the dimension and the Gorenstein index of $X$. Moreover, we present an efficient algorithm for the classification of $d$-dimensional fake weighted projective spaces of Gorenstein index $g$.

Donnerstag, 11.05.2023: The Picard index of a C*-surface

Justus Springer (Universität Tübingen)

By the Picard index of a normal surface, we mean the index of its Picard group inside its divisor class group. For normal rational projective C*-surfaces, we provide a formula for the Picard index in terms of the orders of the local class groups. As an application, we show how to classify log del Pezzo C*-surfaces of given Picard index and present explicit results up to Picard index 10.000. We discuss how this interacts with existing classifications of given Gorenstein index or log terminality.

Donnerstag, 11.05.2023: An energy minimizing flow for rotating stars in GR

Prof. Dr. Helmut Kaul (Universität Tübingen)

Within the framework of general relativity a star model is treated, consisting of a rotating liquid in the equilibrium of gravitational forces, pressure and centrifugal forces. I show the existence of this model using an energy-minimizing flow, assuming the mass and angular velocity are given.

Donnerstag, 11.05.2023: Continuum limit of Bell's Jump Process

Karla Traulsen (Tübingen)

Bell’s jump process was originally introduced for lattice quantum field theory but can be defined for any lattice quantum theory and is a Markov process on a lattice. It has been conjectured by Sudbery and Vink that Bell’s jump process for a lattice approximation to quantum mechanics converges to Bohmian mechanics in the continuum limit in which the lattice width shrinks to zero. In our work we are interested in the mathematical relation between Bell’s process and Bohmian mechanics, more precisely in the possibility of obtaining Bohmian mechanics as a limiting case of Bell’s process. We turn the considerations of Sudbery and Vink into rigorous theorems and prove a precise version of their conjecture for one particle in one dimension.