# Vojtěch Tůma

# REU 2013

Hi! My name is Vojtěch Tůma, and you probably won't be able to pronounce my first name correctly, so you better call me just Vojta (pronounced more like Voyta) or whatever name you like.

I am a member of the group of Czech students participating in the
Research Experience for Undergraduates 2013
at Dimacs, Rutgers.
We are from DIMATIA,
Charles University in Prague
.

I am studying Computer Science (undergraduate)
at Faculty of Maths and Physics, Charles University.

## Work

- Part of my work consists of investigating the so-called Entropy compression method, which was developed by Moser for an algorithmic proof of Lovasz Local Lemma, an important tool in probabilistic method. Since then, this method has found some applications in combinatorics. For an introduction to this topic, see the handout I have prepared for my talk about the method during REU.
My advisor for this project is Mario Szegedy.
- My main area of study are sparse classes of graphs. In particular, I work with the theory of nowhere dense structures developed by Nesetril and Ossona de Mendez. So far, I have co-authored two results which apply this theory to dynamic data structures – one paper deals with counting patterns (e.g., subgraphs) in graphs, the second (written during this REU) deals with dynamic decomposition of graphs.
My (external) advisor for this project is Zdenek Dvorak.
- With my colleague Martin Koutecky I'm working on so-called Neighbourhood diversity. More information can be found on his webpage (as he is the principal investigator of this topic among us).
- With my colleagues Martin Balko and Karel Kral we have written short introductory notes on Combinatorial Discrepancy, based on a talk by Rakghu Meka.
- We were able to solve a problem regarding Bulgarian solitaire, posed in Problems section in American Mathematician Monthly. We plan to submit our solution there, and then put here a link to it.