Summer/Winter Schools

VSM Summer School 2023
September 10 to 16, 2023 in Dienten am Hochkönig
The School takes place at the Universitätssport- und Seminarzentrum Dientnerhof.
The program will start on Monday, September 11 in the morning and
finish on Friday, September 15 in the afternoon. Participants are
expected to arrive on Sunday, September 10 and to stay until Saturday,
September 16. Registration is open until July 31. Registration is open for all student members of the VSM.

Stefanie Sonner from Radboud University, Uli Wagner from IST Austria, and Wadim Zudilin from Radboud University
have already agreed to deliver classes. Please find further details below:

Stefanie Sonner from Radboud University
Degenerate Diffusion Equations and Applications in the Modelling of Biofilms
In this course I will give an introduction to degenerate diffusion equations motivated by models for biofilm growth. Biofilms are dense aggregations of bacterial cells attached to a surface and held together by a self-produced slimy matrix. They affect many aspects of human life and play a crucial role in natural, medical and industrial settings.

We will discuss important properties and mathematical difficulties of degenerate diffusion equations. To this end we will look at the porous medium equation as a prototype example and compare the qualitative behavior of solutions with the qualitative behavior of solutions of the classical heat equation. In particular, we will discuss self-similarity, finite speed of propagation, regularity and travelling wave solutions. Furthermore, we will connect the theory with applications looking at models for bacterial biofilms where degenerate diffusion effects play an important role.

Uli Wagner from IST Austria
Topological Methods in Discrete Mathematics and Theoretical Computer Science
Methods and ideas from algebraic and geometric topology have been applied with great success (and often in very surprising ways) to prove results in combinatorics, discrete geometry, and theoretical computer science. A classical example is the following: What is the minimum number of colours necessary to color all the k-element subsets of an n-element set such that no pair of disjoint sets receive the same color (where n and k are positive integers with n>2k)? In 1978, Lovász used topological methods to prove that the answer is n-2k+2, resolving a conjecture of Kneser from 1955 that at first sight seemed to have no connection to topology.

In this course, we will give an introduction to this interplay between topology and discrete mathematics, which has seen rapid progress in recent years, illustrating it by a variety of topics and problems including topological lower bounds for graph coloring (of which Lovász‘ result is an example), decision-tree complexity and evasiveness of graph properties, and (non)embeddability and Tverberg-type results.

Wadim Zudilin from Radboud University
A Rational Introduction to Irrationality
Though almost every real number happens to be irrational, proving that a particular – and a particularly interesting – number is, often requires very special techniques. This leads to numerous connections of number theory with other mathematics topics including asymptotic analysis, combinatorics of binomial sums, arithmetic of differential equations, tools from computer algebra and many more. The goal of my lectures is to highlight such links and their use in irrationality proofs for special numbers, like π and the values of Riemann’s zeta function at positive integers. We will start our journey with the classical Euclidean algorithm and continued fractions.

VSM Summer School 2022
18-24 September, 2022 in Weißensee

Arnaud Chéritat, Institut de Mathématiques de Toulouse
One Dimensional Dynamics

Mark Peletier, TU Eindhoven
Some Mathematical Aspects of Deep Learning

Karen Vogtmann, University of Warwick
Moduli Spaces of Graphs and Graph Complexes


VSM Summer School 2021
19-25 September, 2021 at Weißensee

Alessandra Iozzi, ETH Zurich
Lattices in SL(n,R), and more…

Joachim Rosenthal, University of Zurich
The mathematical Foundations of Information theory from Claude Shannon
An introduction to Mathematical Coding Theory
An Overview to Public Key Cryptography

Fredi Tröltzsch, TU Berlin
An Introduction to Optimal Control of Partial Differential Equations


VSM Summer School 2020
13-19 September, 2020 at Weißensee

Oswin Aichholzer, TU Graz
Crossing numbers of complete and complete bipartite graphs

Elisa Davoli, TU Wien
Effective theories for composite materials: from two-scale convergence to chirality effects

Philipp Petersen, University of Vienna
Four key ideas in data science and machine learning

VSM Summer School 2019

22-28 September, 2019 at Weißensee

Alin Bostan, INRIA
Efficient experimental mathematics for combinatorics and number theory

Diogo Gomes, KAUST
An introduction to symbolic mathematics with applications to partial differential equations

Alfio Quarteroni, Politecnico di Milano and Ecole Polytechnique Fédérale de Lausanne (EPFL)
Mathematical and numerical models for multi-physics applications

Further Details


VSM Winter School on Quantum Computation
9-15 March, 2019 in Dienten am Hochkönig

Ämin Baumeler, Austrian Academy of Sciences
Introduction to Quantum Computation

Barbara Kraus, Universität Innsbruck
Entanglement Theory

Norbert Schuch, Max Planck Institute of Quantum Optics
Entanglement in Complex Quantum Systems


VSM Summer School 2018
16-22 September, 2018 at Weißensee

László Erdős, IST Austria
Random matrices and disordered quantum systems

Adolfo Quiros Gracián, Universidad Autónoma de Madrid
Elliptic curves and public key cryptography

Hans Schoutens, New York City College of Technology
Ultraproducts at the cross-roads of model-theory, algebra and geometry


VDS Summer School 2017
September 2-8, 2017, Obergurgl

Henry Cohn, MIT & Microsoft Research
Packing in high dimensions

Matthias Kreck, Universität Bonn
A panorama of manifolds in dimensions one to eight

Josef Teichmann, ETH Zürich
Affine processes: theory, applications and new developments


VDS Summer School 2016
September 18-23, 2016, Obergurgl

Eduard Feireisl, Charles University Prague
The Navier-Stokes millennium prize problem

Joseph M. Landsberg (Texas A&M University, College Station)
Uses of geometry in theoretical computer science