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Combinatorial Structures and Processes

The project brings together combinatorialists of various fields with the aim that they will enrich each other’s techniques. The tool kits they will bring include topology, probability, statistical physics and algebra. These should... ver más

31/07/2024

869K€

Presupuesto del proyecto: 869K€

Líder del proyecto

UNIVERZITA KARLOVA No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Ver 7 Participantes

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2024-07-31

MSCA-RISE-2018: Research and Innovation Staff Excha...

I+D

Cerrada hace 6 años

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Información adicional privada

No hay información privada compartida para este proyecto. Habla con el coordinador.

7 Participantes

575.00K€ | Lider

RUTGERS, THE STATE UNIVERSIT...

Simon Fraser University

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Duración del proyecto: 68 meses Fecha Inicio: 2018-11-19
Fecha Fin: 2024-07-31

Líder del proyecto

UNIVERZITA KARLOVA No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 869K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The project brings together combinatorialists of various fields with the aim that they will enrich each other’s techniques. The tool kits they will bring include topology, probability, statistical physics and algebra. These should apply to matching problems (a central topic in combinatorics), algorithmic problems, coloring problems (which are decompositions into independent sets or matchings) and homomorphisms (a generalization of colorings). One umbrella under which many of these can be gathered is the intersection of two matroids, a notion generalizing that of matchings in bipartite graphs. Researchers are baffled by a strange phenomenon – that moving from one matroid to the intersection of two matroids sometimes costs little. The algorithmic problems are indeed harder, but the difference between min and max in the min-max theorems suffer only a conjectured penalty of 1. This connects with a second direction of the research, fine grained complexity, which deals with polynomially solvable problems, and aims to prove, under widely believed assumptions, lower bounds on the exponents in the polynomial bounds. A major question in the field is proving similar tight bounds for approximation problems. A direction connecting matchings, colorings and homomorphisms was initiated recently in statistical physics. It investigates typical algorithmic complexity, of computational problems taken under some probability distribution. While the worst case complexity questions are difficult in general and not clearly practically relevant, when we restrict to a given probability distribution of instances and when we are interested in high probability results, progress has been made, that has contributed also algorithmic insights beyond the probabilistic setting. We propose to address several outstanding open questions from the field. Finally we will work on a deep connection, studied by some of the researchers in the project, between Ramsey theory, Model theory and graph homomorphisms.

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