## 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 office@vsmath.at.

**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 ToulouseOne 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.

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

***

**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