Research interets and projects

  • Combinatorics of convex polytopes and related structures:

    This involves the study of face numbers and flag numbers of polytopes and complexes. Connections with commutative algebra and with intersection homology of toric varieties, relations with polarity and symmetries and further applications in polytope theory are also studied. I am interested in using Algebraic shifting (generic initial ideals) both in the exterior algebra and commutative algebra contexts,

  • Combinatorics of the simplex algorithm for linear programming:

    Research focuses on the study of bounds on the diameter of graphs of polyhedra and on the performance of randomized pivot rules.

  • Threshold phenomena and influences:

    A study is made of sharp transition results for monotone properties under symmetry, related discrete isoperimetric results, relations with random graph theory, percolation, first passage percolation, extremal combinatorics and harmonic analysis.