Local and Global Structure in Measurable Combinatorics (LoGloS)

The project aims to build a unified theory for the study of structural, combinatorial, and algorithmic aspects of local problems on graphs, groups, and Euclidean spaces in both discrete and continuous contexts. This will be done in the framework of measurable combinatorics, a field that lies at the borderline of mathematics (descriptive set theory, random processes, measured group theory, dynamics, limit theory of discrete structures, combinatorics, analysis) and theoretical computer science (distributed computing, property testing, constraint satisfaction problem, complexity theory). See our survey with Z. Vidnyánszky From descriptive to distributed, or the great surveys of Bernshteyn, Pikhurko, and Kechris and Marks on recent development in the area of Measurable Combinatorics.

Concrete topics of the project include the study of countable Borel equivalence relations, combinatorics of Borel graphs, local algorithms in the context of random processes and measurable dynamics, and continuous and discrete tilings.

Open position

We are looking for a postdoctoral researcher to join the LoGloS project. The position is open to candidates interested in any of the research directions described above.

• 3-year fixed-term position
• Salary: 75000 CZK/month
• Starting date: 1 January 2027, or by agreement

Informal inquiries are welcome at grebikj@gmail.com.

Team

PI - Jan Grebik