Summer Term 2020
-
Security and Privacy of Prof. Ralf Küsters at the University of Stuttgart.
Winter Term 2019
-
Introduction to Modern Cryptography of Prof. Ralf Küsters at the University of Stuttgart.
Summer Term 2019
-
Training program for tutors and peer educators in physics and mathematics, April 1st - 3rd, 2019. Lecture notes in german: Tutor Qualification Program 2019.
Winter Term 2018/19
-
Cryptography by Prof. Otto Forster.
You will find further information on the exercise lessons here (german).
Summer Term 2018
-
Training program for tutors and peer educators in physics and mathematics. Lecture notes in german: Tutor Qualification Program 2018.
Winter Term 2017/18
-
The Zeta function and the Riemann Hypothesis by Prof. Otto Forster.
You will find further information on the exercise lessons here (german).
Summer Term 2017
-
No lectures.
Winter Term 2016/17
-
No lectures.
Summer Term 2016
-
Riemann Surfaces by Prof. Otto Forster. You will find further information on the exercise lessons here.
Winter Term 2015/16
-
Algorithmic Number Theory and Cryptography by Prof. Otto Forster. You will find further information on the exercise lessons here (german).
Summer Term 2015
-
Foundations of mathematics II (german) by Dr. Erwin Schörner.
Winter Term 2014/15
-
Foundations of mathematics I (german) by Dr. Erwin Schörner.
Summer Term 2014
-
Linear Algebra II (german) by Dr. Erwin Schörner.
Winter Term 2013/14
-
Analysis III (german) by Prof. Franz Merkl.
Summer Term 2013
-
Analysis II (german) by Prof. Franz Merkl.
Winter Term 2012/13
-
Riemann Surfaces by Prof. Otto Forster.
You will find further information on the exercise lessons here.
Summer Term 2012
-
Linear Algebra II (link no longer available) by Prof. Andreas Rosenschon.
Winter Term 2011/12
-
Linear Algebra I (link no longer available) by Prof. Andreas Rosenschon.
Research
Die multiplikative Verknüpfung in den Verlinde Algebren über SU(2)
Die multiplikative Verknüpfung in den Verlinde
Algebren über SU(2), 2009.
Abstract
We give a purely representation theoretic discription of the multiplicative structure of the Verlinde algebras over the representation ring of SU(2).
Tame Harmonic Bundles on Punctured Riemann Surfaces
Tame Harmonic Bundles on Punctured Riemann Surfaces, 2011.
Abstract
A punctured Riemann surface is a compact Riemann surface with fi nitely many points removed. We will discuss an equivalence by [Sim90] between tame harmonic
bundles, regular filtered stable Higgs bundles resp. D-modules and regular fi ltered local systems over these surfaces.
Moduli Spaces of Parabolic Twisted Generalized Higgs Bundles
Moduli Spaces of Parabolic Twisted Generalized Higgs Bundles, 2015.
Abstract
In this thesis we study moduli spaces of decorated parabolic principal G-bundles on a compact Riemann surface X.
In [Sch08] Alexander Schmitt constructed the moduli space of a ne decorated Higgs bundles consisting of a principal G-bundle P on X and a global section
into an associated vector bundle as a GIT-quotient. Decorated Higgs bundles are generalizations of several well-studied
objects, such as G-Higgs bundles, Bradlow pairs or quiver representations.
In this work we generalize this GIT-construction of the moduli space of decorated Higgs bundles to the case of a ne parabolic decorated Higgs bundles.
A parabolic structure on P over a fi xed fi nite subset S of punctures of the compact Riemann surface X is given by reductions
of into P/P^j where P^j is a parabolic subgroup of G.
Our main result shows the existence of the resulting moduli space of decorated parabolic bundles as a quasi-projective scheme over C.
For a suitable choice of the associating representation, i. e. the adjoint representation of G on its Lie algebra, the moduli spaces of parabolic G-Higgs bundles
(see [Sim94]) is obtained from our construction by slight modi cations of the semistability concept.
Other important applications include the construction of a (generalized) projective Hitchin morphism from the moduli space into an a ffine scheme as well as an extension
of the results of Nikolai Beck [Be14] on moduli spaces of pointwisely decorated principal bundles.