Academy of Mathematics and Systems Science, CAS Colloquia & Seminars Speaker: Prof. Jiajun Wang,California Institute of Technology Title: Nice Heegaard diagrams and combinatorial Floer homology Time: 2010.1.29 9:30am Venue: Room:S509 Abstract: The gauge theory coming from physics has shown great influences in the study of three- and four-dimensional topology in the past thirty years. These include instantons (Donaldson invariants using Yang-Mills equations) and monopoles (Seiberg-Witten invariants using Seibert-Witten equations). In particular, these invariants distinguish different smooth structures on four-manifolds and detect the Thurston norms of three-manifolds. In another direction, Heegaard Floer theory coming from symplectic geometry shows the same properties and is conjectured to be equivalent to them. In this talk, we give a combinatorial theory under development which is equivalent to all these theories (modulo the work in progress of Taubes, Feehan-Leness and others). Affiliation: