New trends from Classical Theorems in Geometry, Combinatorics, and Topology (23w5023)



Imre Bárány (Alfred Renyi Institute of Mathematics)

(Ecole Polytechnique Federale de Lausanne)

(City University of New York)


Eduard Helly proved in 1913 one of the most celebrated results in geometry that gives conditions for the
members of a family of convex objects (with convex boundary and without holes) to have a common point.
Helly's theorem gives rise to numerous generalizations and variants, and is very close related with
the classical theorems of Radon, Caratheodory and Tverberg, which is the r-partite version of Radon's theorem.
All this theorems have a deep connection with many other areas in mathematics such as algebraic topology, discrete geometry, combinatorial geometry, and analysis and could be seen as a multidisciplinary area since it uses tools from, topology, geometry, computer sciences, probability etc. and, in resent years have been useful tool for applications to model problems in real life.
The proposed workshop will assemble the key people senior and students working in this area, in order to explore recent progress and to help focus on future directions of research.