Large discrete structures
The proposed project seeks to introduce novel methods to analyze and approximate large graphs and other discrete structures and to apply the developed methods to solve specific open problems. A need for such methods comes from computer science where the sizes of input structures are often enormous. Specifically, the project will advance the recently emerged theory of combinatorial limits by developing new insights in the structure of limit objects and by proposing a robust theory bridging the sparse and dense cases. The analytic methods from the theory of combinatorial limits will be used to analyze possible asymptotic behavior of large graphs and they will be applied in conjunction with structural arguments to provide solutions to specific problems in extremal combinatorics. The obtained insights will also be combined with methods from discrete optimization and logic to provide new algorithmic frameworks.