Illja Rusakov

I am currently a first-year PhD student at Leipzig University under the supervision of Prof. Łukasz Grabowski. I am a member of the International Max Planck Research School within the Max Planck Institute for Mathematics in the Sciences.

My main mathematical passion lies in geometric group theory. While my earlier studies have focused on group homology and algorithmic aspects, I am now exploring random groups, cost of groups, and other notions from measured group theory.

In 2025, I completed my Master's degree in Mathematics at the University of Regensburg, where I wrote my thesis on Logarithmic Torsion Homology Growth and Computability under the supervision of Prof. Clara Löh. There, I explored a group-homological invariant called torsion growth and computed its behavior under free and direct products.

Conferences

YMCN autumn school: Probability and dynamics on groups, University of Münster, 09/2025.
Regensburg GAP days, University of Regensburg, 07/2025.
Young Geometric Group Theory XIII, University of Copenhagen, 04/2025.
Model Theory Meets Geometric Group Theory, University of Münster, 02/2025.
Metric Topology of Aspherical Spaces, Mathematisches Forschungsinstitut Oberwolfach, 10/2025.
Workshop in Profinite Rigidity, Karlsruhe Institute of Technology, 08/2024.
Homology Growth in Topology and Group Theory, Max Planck Institute Bonn, 05/2024.
Topological and Homological Methods in Group Theory, University of Bielefeld, 03/2024.

Talks

Homological Invariant Growth of Groups, Poster session at the Regensburg GAP days, 07/2025.
Logarithmic torsion homology growth, LKS seminar, University of Regensburg, 07/2025.
Geometric Group Theory meets Model Theory, LKS seminar, University of Regensburg, 03/2025.
Decision trees and the Evasiveness Conjecture, Graphs, Groups, Topology and Computational Complexity seminar, 10/2024.
Every group is a fundamental group, Mathematical communication seminar, 04/2024.
The Higman Embedding Theorem, Decision problems in groups seminar, 01/2024.

Teaching

I have tutored the following exercise classes at the University of Regensburg:

Maths for Media Scientists, 2024.
Foundations of Mathematics, 2023–2024.
Maths for Biologists, 2023.
Linear Algebra I/II, 2022–2023.
Linear Algebra I, 2021.

For the Linear Algebra II class, I have received an Excellence in Teaching award ("Preis für Gute Lehre") by the Dean of Studies.

Contact

Email:

first.lastname{ät}uni-leipzig.de

first.lastname{ät}mis.mpg.de

Office:

Room A523
Augustusplatz 10
Mathematisches Institut
Universität Leipzig

Room G.02
Inselstraße 22
Max-Planck-Institut für
Mathematik in den Naturwissenschaften