Project acronym CRITIQUEUE
Project Critical queues and reflected stochastic processes
Researcher (PI) Johannes S.H. Van Leeuwaarden
Host Institution (HI) TECHNISCHE UNIVERSITEIT EINDHOVEN
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary Our primary motivation stems from queueing theory, the branch of applied probability that deals with congestion phenomena. Congestion levels are typically nonnegative, which is why reflected stochastic processes arise naturally in queueing theory. Other applications of reflected stochastic processes are in the fields of branching processes and random graphs.
We are particularly interested in critically-loaded queueing systems (close to 100% utilization), also referred to as queues in heavy traffic. Heavy-traffic analysis typically reduces complicated queueing processes to much simpler (reflected) limit processes or scaling limits. This makes the analysis of complex systems tractable, and from a mathematical point of view, these results are appealing since they can be made rigorous. Within the large
body of literature on heavy-traffic theory and critical stochastic processes, we launch two new research lines:
(i) Time-dependent analysis through scaling limits.
(ii) Dimensioning stochastic systems via refined scaling limits and optimization.
Both research lines involve mathematical techniques that combine stochastic theory with asymptotic theory, complex analysis, functional analysis, and modern probabilistic methods. It will provide a platform enabling collaborations between researchers in pure and applied probability and researchers in performance analysis of queueing systems. This will particularly be the case at TU/e, the host institution, and at
the affiliated institution EURANDOM.
Summary
Our primary motivation stems from queueing theory, the branch of applied probability that deals with congestion phenomena. Congestion levels are typically nonnegative, which is why reflected stochastic processes arise naturally in queueing theory. Other applications of reflected stochastic processes are in the fields of branching processes and random graphs.
We are particularly interested in critically-loaded queueing systems (close to 100% utilization), also referred to as queues in heavy traffic. Heavy-traffic analysis typically reduces complicated queueing processes to much simpler (reflected) limit processes or scaling limits. This makes the analysis of complex systems tractable, and from a mathematical point of view, these results are appealing since they can be made rigorous. Within the large
body of literature on heavy-traffic theory and critical stochastic processes, we launch two new research lines:
(i) Time-dependent analysis through scaling limits.
(ii) Dimensioning stochastic systems via refined scaling limits and optimization.
Both research lines involve mathematical techniques that combine stochastic theory with asymptotic theory, complex analysis, functional analysis, and modern probabilistic methods. It will provide a platform enabling collaborations between researchers in pure and applied probability and researchers in performance analysis of queueing systems. This will particularly be the case at TU/e, the host institution, and at
the affiliated institution EURANDOM.
Max ERC Funding
970 800 €
Duration
Start date: 2010-08-01, End date: 2016-07-31
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 HARG
Project Harmonic analysis on reductive groups
Researcher (PI) Eric Marcus Opdam
Host Institution (HI) UNIVERSITEIT VAN AMSTERDAM
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary We propose to attack a variety of fundamental open problems in
harmonic analysis on $p$-adic and real reductive groups.
Specifically we seek solutions to the local Langlands conjectures
and various normalization problems of discrete series representations.
For $p$-adic groups, affine Hecke algebras are a major technical tool.
Our understanding of these algebras with unequal parameters has
advanced recently and allows us to address these problems.
We will compute the Plancherel measure on the Bernstein components
explicitly. Using a new transfer principle of Plancherel measures
between Hecke algebras we will combine Bernstein components to form
$L$-packets, following earlier work of Reeder in small rank.
We start with the tamely ramified case, building on work of
Reeder-Debacker. We will also explore these methods for $L$-packets
of positive depth, using recent progress due to Yu and others.
Furthermore we intend to study non-tempered
unitary representations via affine Hecke algebras, extending the
work of Barbasch-Moy on the Iwahori spherical unitary dual.
As for real reductive groups we intend to address essential
questions on the convergence of the Fourier-transform. This theory
is widely developed for functions which transform finitely under a
maximal compact subgroup. We wish to drop this condition in order
to obtain global final statements for various classes of rapidly
decreasing functions. We intend to extend our results to certain types of
homogeneous spaces, e.g symmetric and multiplicity one spaces. For doing
so we will embark to develop a suitable spherical character theory for
discrete series representations and solve the corresponding normalization
problems.
The analytic nature of the Plancherel measure and the correct interpretation
thereof is the underlying theme which connects the various parts of
this proposal.
Summary
We propose to attack a variety of fundamental open problems in
harmonic analysis on $p$-adic and real reductive groups.
Specifically we seek solutions to the local Langlands conjectures
and various normalization problems of discrete series representations.
For $p$-adic groups, affine Hecke algebras are a major technical tool.
Our understanding of these algebras with unequal parameters has
advanced recently and allows us to address these problems.
We will compute the Plancherel measure on the Bernstein components
explicitly. Using a new transfer principle of Plancherel measures
between Hecke algebras we will combine Bernstein components to form
$L$-packets, following earlier work of Reeder in small rank.
We start with the tamely ramified case, building on work of
Reeder-Debacker. We will also explore these methods for $L$-packets
of positive depth, using recent progress due to Yu and others.
Furthermore we intend to study non-tempered
unitary representations via affine Hecke algebras, extending the
work of Barbasch-Moy on the Iwahori spherical unitary dual.
As for real reductive groups we intend to address essential
questions on the convergence of the Fourier-transform. This theory
is widely developed for functions which transform finitely under a
maximal compact subgroup. We wish to drop this condition in order
to obtain global final statements for various classes of rapidly
decreasing functions. We intend to extend our results to certain types of
homogeneous spaces, e.g symmetric and multiplicity one spaces. For doing
so we will embark to develop a suitable spherical character theory for
discrete series representations and solve the corresponding normalization
problems.
The analytic nature of the Plancherel measure and the correct interpretation
thereof is the underlying theme which connects the various parts of
this proposal.
Max ERC Funding
1 769 000 €
Duration
Start date: 2011-03-01, End date: 2016-02-29
Project acronym PLANTIMMUSYS
Project The Plant Immune System: a multidisciplinary approach to uncover how plants simultaneously deal with beneficial and parasitic organisms to maximize profits and protection
Researcher (PI) Cornelis Marinus Jozef Pieterse
Host Institution (HI) UNIVERSITEIT UTRECHT
Call Details Advanced Grant (AdG), LS9, ERC-2010-AdG_20100317
Summary In nature, plants live in complex environments in which they are attacked by a multitude of pathogens and pests. In agriculture this leads to tremendous annual crop losses, representing a value of over 450 billion worldwide. Beneficial associations between plants and other organisms are abundant in nature as well, improving plant growth or aiding plants to overcome biotic or abiotic stress. In the past years, we pioneered research on the complexity of the natural plant immune system that is engaged in interactions of plants with beneficial microbes, pathogens and insect herbivores. We discovered that the plant immune signaling network finely balances the plant¿s response to beneficial and harmful organisms to maximize both profitable and protective functions. As plants have co-evolved with an enormous variety of alien organisms, they harbour a fantastic reservoir of natural defensive mechanisms that until to date remained largely untapped. Here, I propose to mine this undiscovered natural resource in detail, using the Arabidopsis thaliana model system, and an innovative multidisciplinary approach involving a unique combination of state-of-the-art microbial and plant functional genomics, ecogenomics, molecular genetics, cellular biology, computational biology and bioinformatics. The outcomes of the proposed project will provide a detailed understanding of the intrinsic capacity of the plant immune system to simultaneously accommodate mutualists and ward off enemies in order to maximize benefits and minimize damage. Profitably, the discovery of novel plant loci and mechanisms involved in plant immunity will provide multi-faceted possibilities for development of new strategies for sustainable agriculture and resistance breeding of economically relevant crop species.
Summary
In nature, plants live in complex environments in which they are attacked by a multitude of pathogens and pests. In agriculture this leads to tremendous annual crop losses, representing a value of over 450 billion worldwide. Beneficial associations between plants and other organisms are abundant in nature as well, improving plant growth or aiding plants to overcome biotic or abiotic stress. In the past years, we pioneered research on the complexity of the natural plant immune system that is engaged in interactions of plants with beneficial microbes, pathogens and insect herbivores. We discovered that the plant immune signaling network finely balances the plant¿s response to beneficial and harmful organisms to maximize both profitable and protective functions. As plants have co-evolved with an enormous variety of alien organisms, they harbour a fantastic reservoir of natural defensive mechanisms that until to date remained largely untapped. Here, I propose to mine this undiscovered natural resource in detail, using the Arabidopsis thaliana model system, and an innovative multidisciplinary approach involving a unique combination of state-of-the-art microbial and plant functional genomics, ecogenomics, molecular genetics, cellular biology, computational biology and bioinformatics. The outcomes of the proposed project will provide a detailed understanding of the intrinsic capacity of the plant immune system to simultaneously accommodate mutualists and ward off enemies in order to maximize benefits and minimize damage. Profitably, the discovery of novel plant loci and mechanisms involved in plant immunity will provide multi-faceted possibilities for development of new strategies for sustainable agriculture and resistance breeding of economically relevant crop species.
Max ERC Funding
2 500 000 €
Duration
Start date: 2011-03-01, End date: 2017-02-28
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
Project acronym SMEN
Project Single Molecule Enzymology with ClyA Nanopores
Researcher (PI) Giovanni Maglia
Host Institution (HI) RIJKSUNIVERSITEIT GRONINGEN
Call Details Starting Grant (StG), LS9, ERC-2010-StG_20091118
Summary Single molecules based techniques provide the ultimate toolkit to study complex biological systems. In single-molecule approaches, molecules do not need to be synchronised as in ensemble studies, and rare and/or transient species along a reaction pathway as well as heterogeneity and disorder in a sample can be revealed.
Observing and manipulating single molecules, however, is generally complicated, time consuming and withstand several technical limitations that hamper the study of single enzymes to a few selected examples.
Here I am proposing to develop a new technology to study single native enzymes that is sensitive, simple and inexpensive, and has a temporal resolution ranging from few ¼seconds to hours.
Nanopores have been used to detect single molecules and to investigate mechanisms of chemical reactions at the single molecule level. The basic concept of nanopore analysis is to observe, under an applied potential, the disruption of the flow of ions through the pore caused by the interaction of the molecules of interest with a binding site within the pore.
Similarly, small enzymes or functional nucleic acids will be attached to the vestibule of a biological nanopore via disulfide bridge or click chemistry. The conformational changes associated with catalysis will then be observed by the altered ionic flow through the pore. In addition, when a charged chaotropic agent is placed on the trans side of the bilayer, the applied potential will allow the directional control of the flow of the chaotropic agent through the pore that, ultimately, also will control the unfolding and refolding of the protein attached to the pore. This will allow investigations of reversible unfolding processes far from equilibrium at the single molecule level for the first time.
Summary
Single molecules based techniques provide the ultimate toolkit to study complex biological systems. In single-molecule approaches, molecules do not need to be synchronised as in ensemble studies, and rare and/or transient species along a reaction pathway as well as heterogeneity and disorder in a sample can be revealed.
Observing and manipulating single molecules, however, is generally complicated, time consuming and withstand several technical limitations that hamper the study of single enzymes to a few selected examples.
Here I am proposing to develop a new technology to study single native enzymes that is sensitive, simple and inexpensive, and has a temporal resolution ranging from few ¼seconds to hours.
Nanopores have been used to detect single molecules and to investigate mechanisms of chemical reactions at the single molecule level. The basic concept of nanopore analysis is to observe, under an applied potential, the disruption of the flow of ions through the pore caused by the interaction of the molecules of interest with a binding site within the pore.
Similarly, small enzymes or functional nucleic acids will be attached to the vestibule of a biological nanopore via disulfide bridge or click chemistry. The conformational changes associated with catalysis will then be observed by the altered ionic flow through the pore. In addition, when a charged chaotropic agent is placed on the trans side of the bilayer, the applied potential will allow the directional control of the flow of the chaotropic agent through the pore that, ultimately, also will control the unfolding and refolding of the protein attached to the pore. This will allow investigations of reversible unfolding processes far from equilibrium at the single molecule level for the first time.
Max ERC Funding
1 220 474 €
Duration
Start date: 2010-11-01, End date: 2016-10-31
Project acronym SYM-BIOTICS
Project Dual exploitation of natural plant strategies in agriculture and public health: enhancing nitrogen-fixation and surmounting microbial infections
Researcher (PI) Eva Kondorosi
Host Institution (HI) MAGYAR TUDOMANYOS AKADEMIA SZEGEDIBIOLOGIAI KUTATOKOZPONT
Call Details Advanced Grant (AdG), LS9, ERC-2010-AdG_20100317
Summary With an unprecedented increase in the human population, higher agricultural production, enhanced food safety and the protection against alarming rise of antibiotic resistant pathogenic bacteria are amongst the main challenges of this century. This proposal centered on Rhizobium-legume symbiosis aims at contributing to these tasks by i) understanding the development of symbiotic nitrogen fixing cells for improvement of the eco-friendly biological nitrogen fixation, ii) gaining a comprehensive knowledge on polyploidy having a great impact on crop yields and iii) exploiting the strategies of symbiotic plant cells for the development of novel antibiotics. Symbiotic nitrogen fixation in Rhizobium-legume interactions is a major contributor to the combined nitrogen pool in the biosphere. It takes place in root nodules where giant plant cells host the nitrogen fixing bacteria. In Medicago nodules both the plant cells and the bacteria are polyploids and incapable for cell division. These polyploid plant cells produce hundreds of symbiotic peptides (symPEPs) that provoke terminal differentiation of bacteria in symbiosis and exhibit broad range antimicrobial activities in vitro. Permanent generation of polyploid cells is essential for the nodule development. It will be studied whether the complete genome is duplicated in consecutive endocycles, how different ploidy levels affect DNA methylation and expression profile and whether polyploidy is required for the expression of symPEP genes. The activity and mode of actions of symPEPs are in the focus of the proposal; i) how symPEPs achieve bacteroid differentiation and affect nitrogen fixation and ii) whether symPEP antimicrobial activities provide novel modes of antimicrobial actions and iii) whether ¿Sym-Biotics¿ could become widely used novel antibiotics. Their applicability as plant protecting and meat decontaminating agents as well as their in vivo efficiency in mouse septicemia models will be tested.
Summary
With an unprecedented increase in the human population, higher agricultural production, enhanced food safety and the protection against alarming rise of antibiotic resistant pathogenic bacteria are amongst the main challenges of this century. This proposal centered on Rhizobium-legume symbiosis aims at contributing to these tasks by i) understanding the development of symbiotic nitrogen fixing cells for improvement of the eco-friendly biological nitrogen fixation, ii) gaining a comprehensive knowledge on polyploidy having a great impact on crop yields and iii) exploiting the strategies of symbiotic plant cells for the development of novel antibiotics. Symbiotic nitrogen fixation in Rhizobium-legume interactions is a major contributor to the combined nitrogen pool in the biosphere. It takes place in root nodules where giant plant cells host the nitrogen fixing bacteria. In Medicago nodules both the plant cells and the bacteria are polyploids and incapable for cell division. These polyploid plant cells produce hundreds of symbiotic peptides (symPEPs) that provoke terminal differentiation of bacteria in symbiosis and exhibit broad range antimicrobial activities in vitro. Permanent generation of polyploid cells is essential for the nodule development. It will be studied whether the complete genome is duplicated in consecutive endocycles, how different ploidy levels affect DNA methylation and expression profile and whether polyploidy is required for the expression of symPEP genes. The activity and mode of actions of symPEPs are in the focus of the proposal; i) how symPEPs achieve bacteroid differentiation and affect nitrogen fixation and ii) whether symPEP antimicrobial activities provide novel modes of antimicrobial actions and iii) whether ¿Sym-Biotics¿ could become widely used novel antibiotics. Their applicability as plant protecting and meat decontaminating agents as well as their in vivo efficiency in mouse septicemia models will be tested.
Max ERC Funding
2 320 000 €
Duration
Start date: 2011-07-01, End date: 2017-06-30
Project acronym VARIS
Project Variational Approach to Random Interacting Systems
Researcher (PI) Wilhelmus Theodorus Franciscus Den Hollander
Host Institution (HI) UNIVERSITEIT LEIDEN
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary The goal of my mathematical research is to force a breakthrough in solving and understanding a number of long-standing open problems that are rooted in physics and chemistry. My objects of study are systems consisting of a large number of random components that interact locally but exhibit a global dependence. Typically, the components of these systems are subject to a simple microscopic dynamics. The challenge lies in understanding the complex macroscopic phenomena that may arise from this dynamics. Core to my proposal are macroscopic phenomena that are very hard to grasp with heuristic or numerical methods: pinning, localisation, collapse, porosity, nature vs. nurture, metastability, condensation, ageing, catalysis, intermittency and trapping. My main line of attack is to combine large deviation theory, which is a well-established technically demanding yet flexible instrument, with a number of new variational techniques that I have recently developed with my international collaborators, which are based on space-time coarse-graining. My goal is to apply this powerful combination to a number of complex systems that are at the very heart of the research area, in order to arrive at a complete mathematical description. The idea is to use the coarse-graining techniques to compute the probability of the possible trajectories of the microscopic dynamics, and to identify the most likely trajectory by maximising this probability in terms of a variational formula. The solution of this variational formual is what describes the macroscopic behaviour of the system, including the emergence of phase transitions. My proposal focuses on five highly intriguing classes of random interacting systems that are among the most challenging to date: (1) polymer chains; (2) porous domains; (3) flipping magnetic spins; (4) lattice gases; (5) evolving random media. The unique reward of the variational approach is that it leads to a full insight into why these systems behave the way they do.
Summary
The goal of my mathematical research is to force a breakthrough in solving and understanding a number of long-standing open problems that are rooted in physics and chemistry. My objects of study are systems consisting of a large number of random components that interact locally but exhibit a global dependence. Typically, the components of these systems are subject to a simple microscopic dynamics. The challenge lies in understanding the complex macroscopic phenomena that may arise from this dynamics. Core to my proposal are macroscopic phenomena that are very hard to grasp with heuristic or numerical methods: pinning, localisation, collapse, porosity, nature vs. nurture, metastability, condensation, ageing, catalysis, intermittency and trapping. My main line of attack is to combine large deviation theory, which is a well-established technically demanding yet flexible instrument, with a number of new variational techniques that I have recently developed with my international collaborators, which are based on space-time coarse-graining. My goal is to apply this powerful combination to a number of complex systems that are at the very heart of the research area, in order to arrive at a complete mathematical description. The idea is to use the coarse-graining techniques to compute the probability of the possible trajectories of the microscopic dynamics, and to identify the most likely trajectory by maximising this probability in terms of a variational formula. The solution of this variational formual is what describes the macroscopic behaviour of the system, including the emergence of phase transitions. My proposal focuses on five highly intriguing classes of random interacting systems that are among the most challenging to date: (1) polymer chains; (2) porous domains; (3) flipping magnetic spins; (4) lattice gases; (5) evolving random media. The unique reward of the variational approach is that it leads to a full insight into why these systems behave the way they do.
Max ERC Funding
1 930 000 €
Duration
Start date: 2011-05-01, End date: 2016-04-30
