Chennai Mathematical Institute

Seminars




3:30 pm, Seminar Hall
Helly-type theorems and topological combinatorics

Xavier Goaoc
Université Paris-Est Marne-la-Vallée.
24-01-18


Abstract

To study or manipulate a geometric object, it is sometimes useful to consider an associated combinatorial structure, which emphasizes some of its properties. I will illustrate this idea on the analysis of the intersection patterns of subsets of the space. By a theorem of Helly, if four convex sets in the plane intersect triple-wise, then they must have a point in common. This property gives rise to many generalizations, relaxing for example the assumption of convexity. I will discuss how some techniques from topological combinatorics (embeddings of graphs or simplicial complexes, homology of nerve complexes and nerve theorem) allow to unify many of these generalizations.





Google
Search WWW Search cmi.ac.in