Charles University will host the second part of Research Experiences for Undergraduates 2024 from July 22th until August 02nd.
Each day there will be lectures starting at 10 typically until 12.30. During lectures some working problems will be introduced, and the afternoons will be dedicated to working on the problems. The following week July 29- August 2nd there will be the Midsummer Combinatorial Workshop, all REU students participating
Place: Faculty of Mathematics and Physics, Malostranske namesti 2/25, Prague 1
Monday 22/07/2024
Martin Černý: Spectral graph theory with applications
Tuesday 23/07/2024
Martin Balko: Annoying (but beautiful) visibility problems
In this talk, we will survey and explore known problems and conjectures about visibility in point sets in the plane. Here, two points p and q are visible in a planar point set P if there is no point of P lying between p and q on the line segment pq. All these problems have a couple of things in common: they are easy to state but, somewhat annoyingly, are also very difficult to solve and most of them remain open. For example, we will discuss the Blocking conjecture about placing n points in the plane in general position with the smallest number m of blocking points between them so that no
two of the n points are visible in the resulting set of n+m points.
Wednesday 24/07/2024
Irena Penev: Mathematics of Perfect Graphs
The presentation is here.
Thursday 25/07/2024, room S6
Student workshop
10:00 - 10:35 Filip Úradník, Charles University - "Cooperative Game Theory & Optimism Bias"
10:35 - 11:10 Amanda Wang, Princeton University - “Interpolating Valuations for Combinatorial Auctions”
11:10 - 11:20 Break
11:20 - 11:55 Jelena Glišić, Charles University - "Star-Forest Decompositions of Complete (Geometric) Graphs"
11:55 - 12:30 Todor Antić, Charles University - "Slides (and Flips): Reconfigurations of Plane Caterpillars (and Paths)"
Friday 26/07/2024
Jan Volec: Removal lemma and its applications
In this lecture, we first state the triangle removal lemma and present some of its applications in computer science and number theory. Next, we discuss how the triangle removal lemma generalizes to other graphs.
If time permits, we will also mention the generalization of Graph Removal Lemma to t-uniform hypergraphs, and sketch its application to Szemerédi's theorem on k-term arithmetic progressions in subsets of integers with positive upper density.
Posted on 2024-07-21