Transversal, Helly and Tverberg type Theorems in Geometry, Combinatorics and Topology III (16w5064)

Arriving in Oaxaca, Mexico Sunday, October 23 and departing Friday October 28, 2016


Emo Welzl (ETH Zurich)

(École Polytechnique Fédérale de Lausanne)

(National University of Mexico at Queretaro)

Imre Bárány (Alfred Renyi Institute of Mathematics)

(Universidad Nacional Autónoma de México)


In the last years, there has been a significant increase of research activity and productivity in the areas of transversals, Helly and Tverberg type theorems and there have been many active interactions with other fields of mathematics. Notable advances have been made in the development of discrete geometry with the analogue of the notion of graph expansion for higher dimensional simplicial complex, discovered by J. Fox, M. Gromov, V. Laforgue, A. Naor, and J. Pach. Furthermore, there are new ideas to develop in the theory of hyperplane transversal, the theory of colorful theorems, generalizing classical results from convexity. In fact we expect the uncovering of interesting connections with oriented matroid theory and topology. Furthermore, the use of Algebraic Topology and Geometry has been used frequently and has been proved to be a powerful tool in the study and solution of problems in this area, as for example, those problems connected with Mass Partitions and Tverberg-type theorems.

It is important to take advantage now, of all the inertia that this increased research activity is giving us and reunite prominent experts such as I. Barany (Budapest), Welzl, Emo (Zürich (CH)), Pach, Janos (Lausanne (CH)), G. Kalai (Jerusalem), J. Matousek (Prague), L. Montejano (Querétaro), R. Pollack (Courant), H. Tverberg (Bergen) together with well establish mathematicians of all over the world with expertise in several areas of mathematics such as A. Holmsen (Korea), F. Santos (Spain), J. De Loera (USA), T. Biztriczky (Canada), J. Ramirez Alfonsin (France), D. Oliveros (Mexico) as well as the very promising young group of researchers that have been attracted to the field, among these, we mention B. Bukh (Pittsburgh (US)), P. Soberon (Wisconsin), Roldan-Pensado (Querétaro), R. Karasev (Moscow), A. Akopyan (Moscow (RU)), M. Tancer, (Praha (CZ)), We believe that it is now very important to repeat the experience of bring together senior and junior researchers in the increasingly important field of Transversal and Helly-type theorems.

All this research activity was reflected in the successful workshops on Transversal and Helly-type Theorems in Geometry, Combinatorics and Topology I and II that took place at the Banff International Research Station (BIRS), the first one from the 20th to the 25th of September, 2009 and the second one from the 21 until 26 of October in 2012. With a collection of articles in this topic, a special Issue of the Journal ``Discrete and Computational Geometry'' was dedicated to the publication of the most relevant works presented during the first workshop. Given this success and the generated research impetus, as we mention before, it is important to reunite again researchers in the area with the objective of interchanging ideas and assessing recent advances, to further foster awareness of the inter-disciplinary aspect of Transversal and Helly-type Theorems in relation to geometry, topology, combinatorics, and computer science, and to map yet other directions of future research. Our objective is to realize these goals via this workshop.