Summer/Winter Schools

The yearly Summer Schools are a central activity of the VSM, which take place in September each year. They offer a perfect opportunity to meet fellow students and socialize with them and at the same time get an introduction to mathematical topics of broader interest. The VSM also organized a Winter School once, but this is not planned to become a regular activity. 

VSM Summer School 2026
August 31 – September 5, 2026  in Strobl am Wolfgangsee. 
The School will take place at the Bifeb (Bundesinstitut für Erwachsenenbildung).

Confirmed speakers:

• Manuel Bodirsky (TU Dresden)
• Cordula Reisch (Roskilde University)
• Slawomir Solecki (Cornell University)

Detailed Information:
– Manuel Bodirsky (TU Dresden): Complexity of Constraint Satisfaction
Abstract: Constraint satisfaction problems are computational problems that naturally appear in many areas of mathematics and theoretical computer science. One of the central themes is their computational complexity, and in particular the border between polynomial-time tractability and NP-hardness. In recent years, the same border surprizingly reappears as a relevant border in other areas of mathematics, e.g. in algebra, in descriptive complexity, and in topology. In this course we introduce the universal-algebraic approach to study the computational complexity of CSPs. To keep the presentation accessible, we start the course in the beautiful setting of directed graphs and graph homomorphism problems.
– Cordula Reisch (Roskilde University): Mathematical Modeling with Heterogeneous Reaction-Diffusion Equations
Abstract: Many natural phenomena include interactions and dispersal of species or quantities. Reaction diffusion equations provide a mathematical description for such phenomena, allowing for rigorous predictions and visualizations through simulations. This type of partial differential equations has a very rich solution behavior, including pattern formation and traveling wave phenomena. In this course, we will study those solution types related to applications, and discuss, in particular, the influence of parameters, spatial heterogeneity, and domain shape on the occurrence of special solutions. 
Studying the equations requires the connection of various mathematical fields, within analysis and beyond. We will focus on these connections in the problem sessions. 
– Slawomir Solecki (Cornell University): Descriptive Set Theory and its Applications
Abstract: In the first part of the course, I will present the fundamentals of Descriptive Set Theory, focusing on Polish spaces and Borel, analytic, and coanalytic sets, as well as functions between such sets. I will offer a fresh perspective on these classical topics that differs from the standard presentation in the literature. In the second part, I will discuss quotient spaces of sets in the above classes under Borel or analytic equivalence relations. I will present several dichotomy theorems and conjectures, for example, the Harrington–Kechris–Louveau theorem and the $E_1$-dichotomy. Finally, I will discuss applications of Descriptive Set Theory to analysis and/or dynamics.

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