Algebraic methods
* the study of homomorphisms of graphs, with
special emphasis on problems arising from statistical physics
* long range order for graph homomorphisms
* random H-colorings
* phase transitions
Problems of combinatorial geometry
* finite geometries
- blocking sets
- defining sets
* geometric graphs
- Turán-type problems
- generalizations of the Ham Sandwich Theorem
* crossing number of graphs
Application of algebraic geometry
* ideals of infinite point sets
* nonvanishing theorems for combinatorial applications
* geometric construction of norm graphs
* intersections of diagonal hypersurfaces and algebraic varieties
* explicit constructions of extremal objects
* arrangements of algebraic surfaces
* lower bound proofs
* robust computations,
* hidden convexity
* combinatorial characterizations of algebraic sets