Seminar Algebra and Geometry - Spring 2023

It happens usually on Tuesdays from 10:30 to 12:00 in Spiegelgasse 5, Seminarraum 05.002. Some tea takes place before the talk, at 10:00 in Spiegelgasse 1, 6th floor.

Date	Speaker	Title	Abstract
April 27 (Thursday) Alte Uni, Seminarraum -201	Andriy Regeta University of Jena	On the automorphism group of an affine variety	I will discuss properties of the automorphism group of an affine variety. In particular I will discuss some fundamental differences between such a group and algebraic groups as well as groups of birational transformations.
May 9	Alicia Jaquet-Chiffelle Berlin / Neuchâtel	An Algorithm for computing D-Weierstrass Places	Given a certain curve and a point P on this variety, we can look at the pole orders at P of functions defined on this curve. The set of all possible pole orders at P is surprisingly the same for all but finitely many points, namely Weierstrass points. My talk will be mainly based on an article by Florian Hess. His goal was to find an algorithm for computing Weierstrass points. More precisely, he obtained an algorithm for computing D-Weierstrass places. In my talk, I will start by introducing the concepts of algebraic geometry needed to understand the article. Then, I will define what D-Weierstrass places are and give the idea Florian Hess has for computing these places, that is using a link with linear systems. We will stop a while on this link which is a center point of his article and happens to have an error in its proof. Indeed, we have found a counter-example to one of the arguments used in his proof. We showed as well that his proof is correct if we added a new hypothesis. The proposition he states seems however correct in the general case as well, but no proof has been found up till now. Supposing the proposition is correct in the general case, I will then show how he uses this link to obtain an algorithm for computing D-Weierstrass places.
May 30	Pascal Fong Paris-Saclay	tba	tba
June 13	Adrian Langer University of Warsaw	tba	tba
June 30 (Friday)	Isabel Vogt Brown University	tba	tba