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.
Fields of science
- natural sciencesmathematicspure mathematicsarithmetics
- natural sciencesmathematicspure mathematicstopologyalgebraic topology
- natural sciencesmathematicspure mathematicsgeometry
- natural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics
- natural sciencesmathematicsapplied mathematicsstatistics and probability
Call for proposal
ERC-2010-AdG_20100224
See other projects for this call
Funding Scheme
ERC-AG - ERC Advanced GrantHost institution
1053 Budapest
Hungary