## Vorlesung zur Geometrie

Fr 10-12 Uhr NB 6/99

150297 Vorlesung zur Geometrie## Oberseminar "Algebraische Geometrie"

Zeit: Mo 16-18 Uhr NA 2/64

14.11.2011 : Prof. Dr. De-Qui Zhang (U Singapore) "Automorphisms of positive entropy on compact Kahler manifolds"

We show that a minimal compact Kahler manifold (or minimal normal projective variety) X of dimension n > 2 has at most n-1 independent commuting (modulo elements of null entropy) automorphisms of positive entropyand the maximality n-1 occurs only when X is a quotient of a compact torus.

05.12.2011 : Herrn Tarig Abdelgadir Title: "Quivers of sections on toric orbifolds"

Abstract: Despite the importance of linear series in the theory of algebraic varieties, an appropriate analogue for algebraic stacks does not exist. For projective toric orbifolds, we use quivers and generalizations of moduli spaces of quiver representations to give a stacky analogue to linear series. As a further application, we alter our construction to comment on the McKay correspondence.

12.12.2011 : Herr Prof. Dr. Stefan Maubach (Jacobs University, Bremen) "Affine Algebraic Geometry over finite fields"

Abstract: Affine algebraic geometry in its most elementary form, is studying the automorphisms of K[x1,...,x n](K a field), or, equivalently, the polynomial automorphisms Kn ➝ Kn. The main focus has been on K characteristic zero, and then even mainly K= C The case char (K)=p was not a popular object of study (mostly appearing as a free by-product). However, in recent years the interest in the characteristic p topic has gained more and more interest. In this talk, I will narrow my focus even more and try to give a comprehensive overview of all (recent) developments on polynomial automorphisms over finite fields. This topic has nice connections with finite group theory (especially permutation groups), as well as potential for applications in (symmetric) key cryptography. If time permits, I will discuss one such application I recently designed.

19.12.2011 Wald

09.01.2012 Perling

16.01.2012 Ledwig

23.01.2012 Mosch

30.01.2012 Herpel