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13 projets européens trouvés

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 TERMINÉ 

Limits of discrete structures (StrucLim)

Date du début: 1 févr. 2014, Date de fin: 31 janv. 2019,

Built on decades of deep research in ergodic theory, Szemeredi's regularity theory and statistical physics, a new subject is emerging whose goal is to study convergence and limits of various structures.The main idea is to regard very large structures in combinatorics and algebra as approximations of infinite analytic objects. This viewpoint brings new tools from analysis and topology into these su ...
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 TERMINÉ 

Regularity and Irregularity in Combinatorics and Number Theory (REGULARITY)

Date du début: 1 mars 2013, Date de fin: 28 févr. 2018,

"Regularity and irregularity plays a central role in mathematics. In the present research proposal we will select problems from combinatorics and number theory (including additive combinatorics), where regularity and irregularity appear. In some cases we have to deal, e.g., with arbitrary finite or infinite subsets of natural numbers, where the only information we have is their cardinality, namel ...
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 1

 TERMINÉ 

Spectral Theory of Graph Limits (SpTheoryGraphLim)

Date du début: 1 mai 2015, Date de fin: 30 avr. 2017,

The need to understand the behavior of real-life networks made it necessary to work out non-standard graph theoretic tools capable of dealing with a large number of interacting nodes. New mathematical areas emerged, such as graph convergence or parallel algorithms.The proposal suggests the study of the spectral aspects of these areas. The proposed research is built around two core problems that gr ...
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 1

 TERMINÉ 

"DISCRETE AND CONVEX GEOMETRY: CHALLENGES, METHODS, APPLICATIONS" (DISCONV)

Date du début: 1 avr. 2011, Date de fin: 31 mars 2017,

"Title: Discrete and convex geometry: challenges, methods, applicationsAbstract: Research in discrete and convex geometry, using tools from combinatorics, algebraictopology, probability theory, number theory, and algebra, with applications in theoreticalcomputer science, integer programming, and operations research. Algorithmic aspects areemphasized and often serve as motivation or simply dictate ...
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 1

 TERMINÉ 

Low Dimensional Topology in Budapest (LTDBud)

Date du début: 1 avr. 2012, Date de fin: 31 mars 2017,

"Heegaard Floer theory. In this project (in collaboration with P. Ozsváth and Z. Szabó) we plan to extend our earlier results computing various versions of Heegaard Floer homologies purely combinatorially. We also plan to find combinatorial definitions of these invariants (as graded groups). Such results will potentially lead to a combinatorial description of 4-dimensional Heegaard Floer (mixed) ...
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 1

 TERMINÉ 

Graph Convergence and Stochastic Processes on Graphs (GraphConvStoch)

Date du début: 1 févr. 2015, Date de fin: 31 janv. 2017,

The proposal covers the following interconnected topics:1. Benjamini-Schramm limits of finite graphs and stochastic processes on graphs;2. continuity and testability of graph parameters;3. factors of Bernoulli i.i.d. labellings;4. graph sequences from groups.The central object for the proposed research is sequences of sparse graphs (either coming from some random graph model or from Cayley graphs) ...
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 1

 TERMINÉ 

Benjamini-Schramm approximation of Groups and Graphings (BAG)

Date du début: 1 mars 2014, Date de fin: 30 mars 2016,

Large graphs have become central objects in many fields in the last couple of decades: in neural sciences, network sciences (WWW, graph of webpages), social sciences (Facebook) and molecular biology. The standard way to handle large networks is Property Testing: We check only a small number of vertices picked randomly, and we try to learn the properties of the huge graph from this random sample. ...
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 1

 TERMINÉ 

Spectra of random matrices, graphs and groups (SPECTRA)

Date du début: 15 juil. 2013, Date de fin: 14 juil. 2015,

The goal is to understand the connections between the geometric structure of sparse (random) matrices and graphs and their spectra. Specifically, I would like to deepen the connections between three distinct research areas, each having their own set of difficult problems and open questions.The first is the study of random matrices with independent entries, started in the statistics community in th ...
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 1

 TERMINÉ 

Gaps between primes and almost primes. Patterns in primes and almost primes. Approximations to the twin prime and Goldbach conjectures (PRIMEGAPS)

Date du début: 1 nov. 2008, Date de fin: 31 oct. 2013,

"The twin prime conjecture, that n and n+2 are infinitely often primes simultaneously, is probably the oldest unsolved problem in mathematics. De Polignac (1849) conjectured that for every even value of h, n and n+h are infinitely often primes simultaneously. These are the most basic problems on gaps and patterns in primes. Another one is the conjecture of Waring (1770), stating that there are ar ...
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 1

 TERMINÉ 

Comparative Genomics and Next Generation Sequencing (COGANGS)

Date du début: 1 nov. 2010, Date de fin: 28 févr. 2013,

"The activity of genes is absolutely essential for all life – from viruses and bacteria to crops and human beings. Despite the many technological breakthroughs within life science research during the last 20-30 years, we are however still far away from fully understanding the activity of genes and which factor influence (regulates) the gene activity. Such knowledge is, by nature, of very high impo ...
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 6

 TERMINÉ 

Automorphic forms and L-functions (AUTOMORPHIC)

Date du début: 1 mai 2009, Date de fin: 30 avr. 2012,

"Automorphic forms and L-functions have a long tradition in number theory which can be traced back to the classical work of Jacobi, Dirichlet, and Riemann. They make hidden symmetries of integers visible and provide deep links to other branches of mathematics such as algebraic geometry, combinatorics, representation theory, ergodic theory, dynamical systems, and mathematical physics. Gergely Harco ...
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 1

 TERMINÉ 

Invariants of residually finite groups: graphs, groups and dynamics (ResFinGroup)

Date du début: 1 sept. 2009, Date de fin: 31 août 2011,

Group theory is a central principle in mathematics. The set of symmetries of an arbitrary mathematical object forms a group, so groups arise virtually in all areas in mathematics (and also in certain parts of physics and chemistry). An infinite group is called residually finite, if the intersection of its subgroups of finite index is trivial. This means that finite images approximate the group str ...
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 1

 TERMINÉ 

Equivariant topology in algebraic geometry (EquiTop in AlgGeo)

Date du début: 1 juil. 2009, Date de fin: 30 juin 2010,

In physical sciences, a very challenging problem is the understanding of sudden changes caused by smooth alterations of parameters. For instance, water suddenly boils, or ice melts. The back of the camel breaks suddenly under a load of just one more straw. These abrupt changes are not only present in dynamical systems, but also in biology (e.g. population models, cell growth), and human society (e ...
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