The project started on April 1st 2011 and will last until March 31, 2016. Locations are Budapest, Prague, Zurich and London. Our main fields of research are the following:

- Geometric transversal, selection, and incidence problems, including algorithmic complexity of Tverberg's theorem, weak epsilon-nets, the k-set problem, and algebraic approaches to Erdos' unit distance problem.
- Topological methods and questions, in particular topological Tverberg-type theorems, algorithmic complexity of the existence of equivariant maps, mass partition problems, centre point and higher dimensional analogues.
- Lattice polytopes and random polytopes, including Arnold's question in the number of convex lattice polytopes, limit shapes of lattice polytopes in dimension 3 and higher, the variance of random polytopes, comparison of random polytopes and lattice polytopes, the integer convex hull and its randomized version.
- The methods come from combinatorics, algebraic topology, probability theory, number theory, and algebra. There are applications in theoretical computer science, integer programming, computational geometry, and operations research. Algorithmic aspects are emphasized and often serve as motivation or simply dictate the questions

If you are interested in , please contact barany@renyi.hu

## Staff:

- Principal Investigator: Imre Barany
- Coinvestigator: Jiri Matousek
- Coinvestigator: Zoltan Furedi
- Gyula Karolyi
- Rados Radoicic
- Aart Blokhuis
- Attila Csaba Por
- Edgar Roldan Pensado
- Pablo Soberon Bravo
- Aleksandr Magazinov
- Gergely Ambrus
- William Lee Steiger
- Jan Kyncl
- Rolf Schneider
- Jozsef Solymosi
- Abdul Basit

## Visiting researchers:

- Akos Seres
- Alexandr Barvinok
- Roy Meschulam
- Martin Tancer
- Pavle Blagojevic
- Domotor Palvolgyi
- Marek Krcal
- Micha Sharir
- Boris Bukh
- Matthias Reitzner
- Adam Sheffer
- Marek Elias
- Zuzana Safernova
- Shlosman Semen
- Noam Solomon
- Josh Zahl
- Adam Scheffer
- Wlodzimierz Kuperberg
- Eric Sedgwick
- Francis Sergeraert
- Tudor Zamfirescu
- Romero Ana
- Daniel Hug
- Hu Ping
- Martin Berka
- Raz Orit