Ukrainian Summer School in Combinatorics 2025

September 15-19, 2025 at TU Freiberg (Sachsen, Germany)

Invited Speakers

• Marthe Bonamy
• Dan Kráľ
• Volodymyr Nekrashevych
• Danylo Radchenko

Description

This summer school is aimed at PhD students, postdocs, and excellent undergraduate students from across Europe, especially Ukraine, working in combinatorics and related areas. We intend for this summer school to serve especially as a networking opportunity for early-career Ukrainian mathematicians with these research interests.

In addition to the summer school, we will be hosting a one-day satellite workshop aimed at postdocs and more senior researchers (see the tentative schedule below). It is possible to attend any combination of these events.

TU Freiberg, founded in 1765, is a research university located in the Iron Mountains in Saxony (Germany). There are a number of hiking opportunities nearby, such as in the Sächsische Schweiz national park. The summer school venue is also directly adjacent to the historic town centre of Freiberg, which has a variety of restaurants serving traditional German and Czech food, such as Stadtwirtschaft (Einstein themed, traditional Czech food), Himmel und Hölle (if you are up for a surprise), Ratskeller (traditional German food), and Kartoffelhaus (traditional German food, a few vegetarian options as well).

Programme

Tentative schedule:

Minicourse Descriptions

1. MONDAY: Introduction to the theory of combinatorial limits
   Speaker: Dan Kráľ
   Description: The theory of combinatorial limits provide analytic tools to represent and analyze large discrete objects. Such tools have found important applications in various areas of computer science and mathematics. One of the most prominent areas of such applications is extremal combinatorics. During this minicourse, we will introduce basic concepts from the theory of combinatorial limits and present applications of the methods provided by the theory of combinatorial limits in the settings of graphs and permutations.


2. TUESDAY: Around Borsuk's conjecture
   Speaker: Danylo Radchenko
   Description: In 1932 Borsuk asked whether any bounded subset of an n-dimensional Euclidean space can be partitioned into (n+1) sets of smaller diameter. In dimensions 2 and 3 the answer to Borsuk's question is affirmative, as was proven by Borsuk himself (for n=2) and Perkal (for n=3), but in 1993 Kahn and Kalai proved that the answer is negative in all sufficiently large dimensions. Nevertheless, many questions remain, both regarding the smallest dimension in which the answer to Borsuk's question is negative, and regarding the behavior of the Borsuk number in large dimensions. In this mini-course I will give an overview of Borsuk's conjecture and some of the surrounding topics, including the counterexample of Kahn-Kalai for large dimensions, the counterexample of Bondarenko, the upper bound due to Schramm, and related questions on Euclidean and spherical bodies of constant width.


3. WEDNESDAY: Coarse graph theory and asymptotic dimension
   Speaker: Marthe Bonamy
   Description: We will discuss graph theory through a "coarse" lens, which allows bounded radius noise. This is connected to the notion of asymptotic dimension, introduced in 1993 by Gromov in the context of geometric group theory. We will define and gently introduce that notion, explaining the connections with coarse graph theory as well as applications for distributed graph algorithms. We will also survey coarse extensions of standard theorems from structural graph theory.


4. THURSDAY: Fractals and group theory
   Speaker: Volodymyr Nekrashevych
   Description: Fractals, such as Julia sets, even if they have complicated geometry, can often be defined using finite combinatorial objects. We will discuss various equivalent forms of such combinatorial descriptions and the rich group theory behind them. This subject has interesting connections with algebra, theory of finite automata, complex analysis, symbolic dynamical systems, and other areas of mathematics.

Satellite Workshop

Programme (TBC, all four invited speakers will deliver a plenary lecture plus talks from other participants)

Ukrainian Prize in Combinatorics

At the satellite workshop, we will award the Ukrainian Prize in Combinatorics. It will be awarded to a researcher with connections to Ukraine who must not have obtained a PhD more than 7 years ago. The prize of 1000 Euros is funded by TU Freiberg and "EdUp – Support and Expansion of the Ukrainian Higher Education Sector in the Area of Resources and Technology". The selection committee consists of Marthe Bonamy, Johannes Carmesin, Dan Kráľ, Oleg Pikhurko, Volodymyr Nekrashevych and Danylo Radchenko. Please do consider to suggest candidates via email to Johannes Carmesin. To nominate a candidate, it suffices to write a short sentence, and add a link to their personal webpage or attach a CV. We may later reach out to aquire more information. You will receive a confirmation email that we received your nomination. Please submit your nomination by July 10th.

Registration

Please register as early as possible (to help us with the planning). It is possible to sign up for the summer school, the satellite workshop, or both. If you sign up for the satellite workshop, please indicate whether you would be interested in giving a talk. Also, if you are a postdoc or more senior researcher, please consider contributing an open problem for one of the problem solving sessions at the summer school; please notify us via email if you would like to do so.

The registration deadline is July 25th.

In order to register, please write an email to Mrs Löschner. NOTE: from June 30th to July 18th, please register by writing an email to Matthew Kroeker.

Funding

There is no conference fee. We have a non-negligible amount of funding to support travel and accommodation. Our sponsors are TU Freiberg and "EdUp – Support and Expansion of the Ukrainian Higher Education Sector in the Area of Resources and Technology", and further funding may be available via DAAD. Priority will be given to Ukrainian participants.