I'm happy to supervise student projects, including as part of a software project (SP, "ročníkový projekt" in Czech), bachelor thesis, and/or master thesis. Broadly, the possible projects fit into 2 categories:
Variants of the Moran process on graphs, and
Finding optimal strategies for specific games.
See below for details. If you are interested in working on some of those projects, please send me an e-mail.
Moran process is a certain random process that models how two colors "fight" against each other via edges of a given graph. Understanding how the graph structure influences the outcome of the process is one of my primary research interests. You can get some idea of what this feels like from looking at these slides, this poster, or my past papers.
A typical student project investigates some variant of the Moran process. Those projects are typically suitable for all of the software project, bachelor thesis, and master thesis.
Moran process with uncoupled births and deaths (master)
Fixation times from different nodes (SP/bachelor/master)
Mutation accumulation (bachelor/master)
Robust and adversarial amplifiers (bachelor/master)
Optimal strategies in Moran process with smart individuals (SP/bachelor)
...
M. Pecho (bachelor thesis): Moranův proces s vnímavými jedinci
R. Jaworski (SP + bachelor thesis): Různé způsoby šíření pro Moranův proces na přímce
T. Varga (SP): Moranův proces na upstream-downstream grafech
K. Doubkova (SP): Distributing the mutant fitness
J. Kotovsky (SP): Optimizing the mutant frequency at time T
L. Kopfova (master thesis): Fixation time in Moran process under strong selection
I'm also interested in bidding games (see e.g. this paper or this paper), or two-player games in general. A typical student project in this direction would "solve" some specific game by implementing an algorithm that finds the optimal strategy to play that game. Those projects are more suitable for the software project, but an extension to a bachelor thesis is possible if the student proves some results based on what the optimal strategy suggested.
Three-state POMDP (SP/bachelor)
Crystallize (SP/bachelor)
Finding a connected battleship (SP/bachelor/master)
...
A. Jahoda (SP): Variace na hru Hádej slova
M. Stojnic (SP): One-dimensional Battleship
S. Kotsiubynska (SP): Finding a treasure first
O. Dvorakova (SP): Variace na hru Ohanami
O. Kravchenko (SP): Pirate dice
S. Sorger (SP): Variace na hru Goblici Jedlici