## 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 UniversityDegenerate 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 AustriaTopological 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 UniversityA 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

***

**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