Project acronym DISCONV
Project DISCRETE AND CONVEX GEOMETRY: CHALLENGES, METHODS, APPLICATIONS
Researcher (PI) Imre Barany
Host Institution (HI) MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary 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.
Summary
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.
Max ERC Funding
1 298 012 €
Duration
Start date: 2011-04-01, End date: 2017-03-31
Project acronym EPIDELAY
Project Delay differential models and transmission dynamics of infectious diseases
Researcher (PI) Gergely Röst
Host Institution (HI) SZEGEDI TUDOMANYEGYETEM
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary The aim of this project is to develop and analyse infinite dimensional dynamical models for the transmission dynamics and propagation of infectious diseases. We use an integrated approach which spans from the abstract theory of functional differential equations to the practical problems of epidemiology, with serious implications to public health policy, prevention, control and mitigation strategies in cases such as the ongoing battle against the nascent H1N1 pandemic.
Delay differential equations are one of the most powerful mathematical modeling tools and they arise naturally in various applications from life sciences to engineering and physics, whenever temporal delays are important. In abstract terms, functional differential equations describe dynamical systems, when their evolution depends on the solution at prior times.
The central theme of this project is to forge strong links between the abstract theory of delay differential equations and practical aspects of epidemiology. Our research will combine competencies in different fields of mathematics and embrace theoretical issues as well as real life applications.
In particular, the theory of equations with state dependent delays is extremely challenging, and this field is at present on the verge of a breakthrough. Developing new theories in this area and connecting them to relevant applications would go far beyond the current research frontier of mathematical epidemiology and could open a new chapter in disease modeling.
Summary
The aim of this project is to develop and analyse infinite dimensional dynamical models for the transmission dynamics and propagation of infectious diseases. We use an integrated approach which spans from the abstract theory of functional differential equations to the practical problems of epidemiology, with serious implications to public health policy, prevention, control and mitigation strategies in cases such as the ongoing battle against the nascent H1N1 pandemic.
Delay differential equations are one of the most powerful mathematical modeling tools and they arise naturally in various applications from life sciences to engineering and physics, whenever temporal delays are important. In abstract terms, functional differential equations describe dynamical systems, when their evolution depends on the solution at prior times.
The central theme of this project is to forge strong links between the abstract theory of delay differential equations and practical aspects of epidemiology. Our research will combine competencies in different fields of mathematics and embrace theoretical issues as well as real life applications.
In particular, the theory of equations with state dependent delays is extremely challenging, and this field is at present on the verge of a breakthrough. Developing new theories in this area and connecting them to relevant applications would go far beyond the current research frontier of mathematical epidemiology and could open a new chapter in disease modeling.
Max ERC Funding
796 800 €
Duration
Start date: 2011-05-01, End date: 2016-12-31
Project acronym POTENTIALTHEORY
Project Potential theoretic methods in approximation and orthogonal polynomials
Researcher (PI) Vilmos Totik
Host Institution (HI) SZEGEDI TUDOMANYEGYETEM
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary The project is aimed at systematic applications of potential theoretical
methods in approximation theory and in the theory of orthogonal polynomials.
Various open problems are proposed in different fields which
can be attacked with tools that have been developed in the
near past or are to be developed within the project.
The main areas are asymptotic behavior of Christoffel functions on the
real line and on curves, the universality problem in random matrices,
orthogonal polynomials and their zeros, polynomial inequalities, approximation
by homogeneous polynomials and some
questions in numerical analysis. The research problems and areas
discussed in the proposal are intensively investigated in current research. As has been the
case in the past, PhD students will be actively involved in the project.
Summary
The project is aimed at systematic applications of potential theoretical
methods in approximation theory and in the theory of orthogonal polynomials.
Various open problems are proposed in different fields which
can be attacked with tools that have been developed in the
near past or are to be developed within the project.
The main areas are asymptotic behavior of Christoffel functions on the
real line and on curves, the universality problem in random matrices,
orthogonal polynomials and their zeros, polynomial inequalities, approximation
by homogeneous polynomials and some
questions in numerical analysis. The research problems and areas
discussed in the proposal are intensively investigated in current research. As has been the
case in the past, PhD students will be actively involved in the project.
Max ERC Funding
402 000 €
Duration
Start date: 2011-01-01, End date: 2016-12-31
