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.
April 27
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
tba tba
June 13 Adrian Langer
University of Warsaw
tba tba
June 30
Isabel Vogt
Brown University
tba tba