CoSP (823748)

  https://cordis.europa.eu/project/id/823748

  Horizon 2020 (2014-2020)

  Combinatorial Structures and Processes

  Research and Innovation Staff Exchange (MSCA-RISE-2018)

  mathematical logic  ·  topology  ·  algebra  ·  graph theory  ·  combinatorics

  2019-01-01 Start Date (YY-MM-DD)

  2024-07-31 End Date (YY-MM-DD)

  € 869,400 Total Cost


  Description

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.


  Complicit Organisations

1 Israeli organisation participates in CoSP.

Country Organisation (ID) VAT Number Role Activity Type Total Cost EC Contribution Net EC Contribution
United States Los Alamos National Security LLC (984384422) nan partner PRC € 0 € 0 € 0
United States TRUSTEES OF PRINCETON UNIVERSITY (999515355) nan partner HES € 4,600 € 0 € 0
Canada Simon Fraser University (986276989) nan partner HES € 9,200 € 0 € 0
Czechia UNIVERZITA KARLOVA (999923434) CZ00216208 coordinator HES € 667,000 € 547,400 € 547,400
Israel TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY (999907720) IL557585585 participant HES € 92,000 € 92,000 € 92,000
France CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS (999997930) FR40180089013 participant REC € 110,400 € 110,400 € 110,400
United States RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY (999882403) nan partner HES € 105,800 € 0 € 0