Students participating in CoSP training organize a yearly CoSP student workshop. This year, it will take place at CUNI 27.7.2023. The student workshop will take place at Malostranské náměstí 2/25, Prague 1, 2nd floor, room S6. The agenda is:

**10:00 - 10:45 Guillermo Gamboa: Sparse metric hypergraphs**

Abstract: Given a metric space (X,d), we say y is between x and z if d(x,z)=d(x,y)+d(y,z). A metric space gives rise to a 3-uniform hypergraph that has as hyperedges those triples {x,y,z}, where y is between x and z. Such hypergraphs are called metric. In this talk, we will consider the other direction: Is any given a 3-uniform hypergraph metric? We will present some examples of metric and non metric 3-uniform hypergraphs, as well as introduce a notion of sparsity for these. Finally, we will prove that such sparse 3-uniform hypergraphs are metric.

**10:45 - 11:30 Caleb Fong: Compactness in Combinatorics**

Abstract: For many combinatorial problems which have been resolved in the finite setting, a natural question is whether similar results hold in the infinite setting. For these questions, the compactness theorem from first-order logic sometimes comes in handy. In this mostly expository talk, we will explain this theorem, talk about its applications and deficiencies, and (if time permits) talk about a research problem which made me care about compactness in the first place.

**11:30 - 12:15 Sumi Vora: A Theoretical Survey of Graph Neural Networks (GNNs)**

Abstract: Graph Neural Networks (GNNs) are a type of deep learning model that can operate on graph structured data. In this talk we provide a survey of the theoretical foundations for graph neural networks, deriving the necessary formulas for updating node embeddings and minimizing loss. We’ll conclude with a discussion of algorithms for fairness and explainability for GNNs.

12:15 - 14:00 Lunch break

**14:00 - 14:45 Jakub Petr: Automorphisms of the Symmetric Groups**

Abstract: We will go over the basics of Group Theory and get to know the notion of automorphisms. At last, we will show why S_6 is the only symmetric group that can have an outer automorphism.

**14:45 - 15:30 Gaurav Kucheriya: Turán-type problems in edge-ordered graphs**

Abstract: The main objective of Turán-type graph problems is to maximize the number of edges a graph can have under certain (forbidding) conditions. This talk will give an overview of some popular results in this field. In particular, we will also see the extension of this problem to edge-ordered graphs. Joint work with Gabor Tardos.

*Posted on 2023-07-26*