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DISCRETE AND CONVEX GEOMETRY: CHALLENGES, METHODS, APPLICATIONS

Objective

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.

Field of science

  • /natural sciences/mathematics/pure mathematics/arithmetic
  • /natural sciences/mathematics/applied mathematics/statistics and probability
  • /natural sciences/mathematics/pure mathematics/topology/algebraic topology
  • /natural sciences/mathematics/pure mathematics/geometry
  • /natural sciences/computer and information sciences

Call for proposal

ERC-2010-AdG_20100224
See other projects for this call

Funding Scheme

ERC-AG - ERC Advanced Grant

Host institution

RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Address
Realtanoda Street 13-15
1053 Budapest
Hungary
Activity type
Other
EU contribution
€ 1 298 012,28
Principal investigator
Imre Barany (Dr.)
Administrative Contact
Tiziana Del Viscio (Ms.)

Beneficiaries (1)

RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Hungary
EU contribution
€ 1 298 012,28
Address
Realtanoda Street 13-15
1053 Budapest
Activity type
Other
Principal investigator
Imre Barany (Dr.)
Administrative Contact
Tiziana Del Viscio (Ms.)