Paul A. Seidel

Works in symplectic topology and mathematical aspects of mirror symmetry. Merges Lefschetz' topological approach (as renewed by Donaldson, his thesis advisor) with Kontsevich's and Fukaya's flavour of noncommutative geometry. This has numerous applications to symplectic topology: exotic symplectic structures on Euclidean spaces; knot invariants (jointly with Ivan Smith); structure of Lagrangian submanifolds (in part, jointly with Fukaya and Smith). One success of this methods is the verification of Kontsevich's Homological Mirror Symmetry conjecture for the quartic surface. His monograph on Fukaya categories and Picard-Lefschetz theory contains a careful account of many basic tools in the field, both algebraic and geometric ones.