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Combinatorial Structures and Processes

Objective

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.

Field of science

  • /natural sciences/mathematics/pure mathematics/algebra
  • /natural sciences/mathematics/pure mathematics/topology

Call for proposal

H2020-MSCA-RISE-2018
See other projects for this call

Funding Scheme

MSCA-RISE - Marie Skłodowska-Curie Research and Innovation Staff Exchange (RISE)

Coordinator

UNIVERZITA KARLOVA
Address
Ovocny Trh 560/5
116 36 Praha 1
Czechia
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 529 000

Participants (2)

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Israel
EU contribution
€ 110 400
Address
Senate Building Technion City
32000 Haifa
Activity type
Higher or Secondary Education Establishments
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France
EU contribution
€ 110 400
Address
Rue Michel Ange 3
75794 Paris
Activity type
Research Organisations

Partners (4)

Simon Fraser University
Canada
Address
University Drive 8888
V5A 1S6 Burnaby
Activity type
Higher or Secondary Education Establishments
Los Alamos National Security LLC
United States
Address
Ms 187
87545 Los Alamos Nm
Activity type
Private for-profit entities (excluding Higher or Secondary Education Establishments)
TRUSTEES OF PRINCETON UNIVERSITY
United States
Address
Nassau Hall 1
08544-2001 Princeton, Nj
Activity type
Higher or Secondary Education Establishments
RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY
United States
Address
Rutgers Plaza 3
08901 New Brunswick
Activity type
Higher or Secondary Education Establishments