Research Interests: Algebraic Topology and its Applications.

I am an algebraic topologist specialising in homotopy theory with research interests focusing on modern homotopy theory (with an emphasis on unstable homotopy) and its applications in Topology, Algebra and Geometry and lately in Power System Engineering. In particular, my research is centred on decompositions and exponent problems in homotopy theory, homotopy aspects of toric topology, Hopf algebras, and on more geometric problems related to cobordisms and string topology.

Homotopy decompositions: A great deal of modern research in homotopy theory deals with decomposition methods. The idea is simple: given a topological space X, decompose it as a product X= A x B, up to homotopy equivalence. The factors should be simpler spaces which are easier to analyse, and their properties let one deduce properties of the original space X. I am active in the rapidly developing area of (functorial) decompositions of loop spaces, which is currently the strongest approach for attacking the homotopy exponent problem. Particularly interesting is the problem of calculating the homology of the atomic retract containing the bottom cell of the loop suspension. Although this problem is interesting in its own right, its solution will provide an important link between algebraic topology and representation theory.

Toric Topology: Toric topology, a newly established area which has at its centre the theory of torus actions on manifolds, emerged at the beginning of the century as an exciting field on the border of topology, algebraic and symplectic geometry, combinatorial and commutative algebra, and combinatorics. My main goal in this area is to associate to certain objects introduced in combinatorics and algebra "topological models" and then study these from the point of view of homotopy theory. I studied the unstable homotopy type of the complement of a complex coordinate subspace arrangement by fathoming out the connection between its topological and combinatorial structures. One consequence of that result is an application in commutative algebra: certain local rings are proved to be Golod.