Welcome to my academic haven! I am Jan and I live in Slovakia with my wife Anna and I’m interested in how the reality works at the deepest levels.
PhD student
Department of Applied Informatics
Comenius University in Bratislava
Slovakia
Curriculum Vitae · Publications & Talks · Teaching & Supervision · Projects, Grants & Awards · Outreach
research
Most of my work comes back to one question: how much of a structure’s global behaviour is already settled by its local parts? In graph theory this becomes very concrete. A graph can be completely rigid — asymmetric, with no nontrivial automorphism — and yet still be full of partial symmetries: small pieces that could be swapped if you only ever looked at them locally. I study those partial automorphisms, the inverse monoids they form, and how far you have to look before a local symmetry either extends to a global one or breaks. That “how far” is what I call asymmetric depth, and it runs straight into the Weisfeiler-Leman algorithm and the graph isomorphism problem, where the same tension between local refinement and global structure decides what is computationally visible at all.
Sparsity is where this stops being abstract. Real networks — brains among them — are sparse, because connections cost something, and sparse classes are exactly where these bounds get sharper; that is the direction the work has been moving.
What keeps me interested is that this question is not really about graphs. When local rules do and do not determine global states is the emergence question, and I have come at it from a few directions — agent-based models of social cohesion, cognitive science, and quantum nonlocal games, where local measurements constrain global correlations in ways classical intuition gets wrong. More recently I have been asking what automated reasoning and machine learning can contribute: not as a substitute for proof, but as a way to search structure spaces far too large to explore by hand, and then to formalize what survives.
research interests
- algebraic graph theory, particularly graph isomorphism problem, asymmetric graphs and partial automorphism inverse monoids of graphs
- complex adaptive systems, particularly “how can emergent states appear in complex systems?”
- AI for mathematics, particularly automated conjecturing, refutation and formalization
- cognitive science, particularly semantic structure in embedding spaces and the history of the field
- quantum nonlocal games, particularly reinforcement learning for violating Bell inequalities
further interests
- history and philosophy of science and mathematics