Organizers: S. Akbulut (MSU) , A. Akhmedov (UMN), D. Auroux (Berkeley), Y. Eliashberg (Stanford), K. Honda (USC), C. Karakurt (UT Austin), P. Ozsváth (Princeton).
The main focus of this workshop will be on holomorphic curve techniques in low-dimensional topology and symplectic geometry. The workshop is a part of the FRG: Collaborative Research: Topology and Invariants of Smooth 4-Manifolds. It is funded by NSF Focused Research Grant DMS-1065955. Additional funds come from the Stanford University Mathematics Research Center. There will be one week of mini-courses, primarily for graduate students, followed by a conference during the second week.Abstract of mini courses :
4-manifolds via their handlebodies (by Selman Akbulut)
Abstract:
Handlebody descriptions of 3 and 4-manifolds will be discussed, and as time permits their various applications to 4-manifold problems will be given, such as carving, branch coverings, knot complements, complex surfaces, Stein manifolds, Lefschetz fibrations, BLF's, corks and plugs. From these techniques various exotic manifolds will be constructed, such as going from handlebody of logarithmic transforms to Dolgachev surfaces, and from handlebody of surface bundles over surfaces to Akhmedov-Park exotic manifolds.
Symplectic topology of Weinstein manifolds (by Yasha Eliashberg)
Abstract:
Weinstein manifolds are symplectic counterparts of affine complex manifolds. We discuss in the lectures techniques (due to Bourgeois, Ekholm and the lecturer) for computation of symplectic invariants of Weinstein manifolds via their handlebody decompositions.
The geometry and physics of Knot Homologies (by Sergei Gukov)
Abstract:
HF=ECH via open book decompositions (by Ko Honda)
Abstract:
The goal of this minicourse is to give a brief introduction to Heegaard Floer homology (due to Ozsvath-Szabo) and embedded contact homology (due to Hutchings), and to prove the equivalence between the two homology theories. The equivalence is joint work with Vincent Colin and Paolo Ghiggini.
Computing with bordered Heegaard Floer homology (by Robert Lipshitz)
Abstract:
Heegaard Floer homology is an extension of the Seiberg-Witten invariants of closed 4-manifolds to invariants of closed 3-manifolds and 4-manifolds with boundary. Bordered Heegaard Floer homology is a further extension, to closed surfaces and 3-manifolds with boundary. We will start by discussing the formal structure of bordered Heegaard Floer homology and discuss how it is defined in a toy model. We will then sketch the definitions in general and spend the rest of the time discussing various ways it can be used for computations. (This is joint work with Peter Ozsvath and Dylan Thurston.)
Pseudoholomorphic quilts and low dimensional topology (by Katrin Wehrheim)
Abstract:
I will give an introduction to Lagrangian correspondences and
holomorphic quilts, their analysis, and some sample applications in
both symplectic topology and the construction of 3- and 4-manifold
invariants.
Thanks to the generous support of the National Science Foundation and the Stanford University Mathematics Research Center, funds are available for partial support of participant expenses. Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Applicants are requested to register, send a CV, including a brief description of research interests, and have one reference letter sent to akhmedov@math.umn.edu. The reference letter is optional for people more than two years after receiving a Ph.D. ***Please note that we are no longer accepting application*** .
James Allen, University of Minnesota |