Summer/Winter Schools

VSM Summer School 2022
18-24 September, 2022 in Weißensee
The School takes place at Hotel Regitnig. The programme will start on Monday, September 19 in the morning and finish on Friday, September 23 in the afternoon. Participants are expected to arrive on Sunday, September 18 and to stay until Saturday, September 24. Registration is open until July 31. If you are interested in participating, please contact

Arnaud Chéritat from the Institut de Mathématiques de Toulouse, Mark Peletier from TU Eindhoven, and Karen Vogtmann from the University of Warwick
have already agreed to deliver classes. Please find further details below:

Arnaud Chéritat, Institut de Mathématiques de Toulouse
One Dimensional Dynamics
This course will be an introduction to dynamical system through a famous example: iteration of the family of maps $f(x)=a.x.(1-x)$.

Basic notions will be defined, observations made. We will prove some of them and give hints of the method of proof of some others. We will also present open conjectures.

According to the amount of time available, we plan to cover a selection of the following notions:
– local dynamics (analysis)
– kneading invariant (combinatorics and topology)
– entropy
– renormalization
Mark Peletier, TU Eindhoven
Some Mathematical Aspects of Deep Learning
In these lectures I want to give an introduction to some of the mathematical challenges associated with deep neural networks. This is a beautiful but still badly understood body of methods, tools, and techniques, in which there is much room for mathematics to provide insight.

I will divide the lectures into three parts:
1. Approximation theory for neural networks: Function classes, the universal approximation property, and the role of depth
2. The practice of finding good parameter points: convex and non-convex optimisation, metastability, the role of overparametrization, the role of the size of the noise
3. Wasserstein geometry in deep learning: how the infinite-width makes the landscape simpler, more convex; using log-Sobolev inequalities to study convergence properties of training algorithms. 

Karen Vogtmann, University of Warwick
Moduli Spaces of Graphs and Graph Complexes
Finite graphs describe phenomena in many areas of mathematics and  science. Often specifying some additional structure allows us to make the set of graphs with this structure into a topological space, called a moduli space of graphs. Graph complexes, on the other hand, are algebraic objects (chain complexes) associated to finite graphs with some specified additional structure. Graph complexes  were introduced by Kontsevich in his work on deformation quantization, but have proved to have applications in a wide variety of other areas. These include the study of groups that are important in low-dimensional topology such as automorphism groups of free groups and surface mapping class groups, which act naturally on moduli spaces of graphs. In this course I will describe several flavors of graph complexes and explain how they are related to each other, to various moduli spaces of graphs  and to the relevant groups.  


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