DISCRETE AND CONVEX GEOMETRY: CHALLENGES, METHODS, APPLICATIONS

Objetivo

Title: Discrete and convex geometry: challenges, methods, applications
Abstract: Research in discrete and convex geometry, using tools from combinatorics, algebraic
topology, probability theory, number theory, and algebra, with applications in theoretical
computer science, integer programming, and operations research. Algorithmic aspects are
emphasized and often serve as motivation or simply dictate the questions. The proposed
problems can be grouped into three main areas: (1) Geometric transversal, selection, and
incidence problems, including algorithmic complexity of Tverberg's theorem, weak
epsilon-nets, the k-set problem, and algebraic approaches to the Erdos unit distance problem.
(2) Topological methods and questions, in particular topological Tverberg-type theorems,
algorithmic complexity of the existence of equivariant maps, mass partition problems, and the
generalized HeX lemma for the k-coloured d-dimensional grid. (3) Lattice polytopes and random
polytopes, including Arnold's question on the number of convex lattice polytopes, limit
shapes of lattice polytopes in dimension 3 and higher, comparison of random polytopes and
lattice polytopes, the integer convex hull and its randomized version.

Ámbito científico

Régimen de financiación

ERC-AG - ERC Advanced Grant

Institución de acogida

HUN-REN RENYI ALFRED MATEMATIKAI KUTATOINTEZET

Aportación de la UE

€ 1 298 012,28

Dirección

REALTANODA STREET 13-15
1053 Budapest
Hungría

Región

Közép-Magyarország Budapest Budapest

Tipo de actividad

Other

Investigador principal

Imre Barany (Dr.)

Contacto administrativo

Tiziana Del Viscio (Ms.)

Enlaces

Contactar con la organización Sitio web

Coste total

Sin datos

Beneficiarios (1)