On the Category of Graphs - complexity, logic and combinatorial aspects
Jaroslav Nešetřil, Univerzita Karlova

The study of categorial properties of combinatorially defined large objects is presently one of the most active areas of structural combinatorics. Homomorphisms of graphs (and of finite structures) capture key problems of statistical physics, constraint satisfaction problems (CSP) and several key areas of computer science (such as property testing).
Topics which I intend to cover include:
 - characterization of primal and dual homomorphism functions (in the context of CSP and statistical physics);
 - universal objects and homomorphism dualities - homomorphism order: existence vs counting.
The area is rich in interesting problems which are accessible to students and postdocs.