SCHEDULE (preliminary)

11:00, March 15, Vincent 113
Conan Leung
Remarks on G_2 geometry

11:00, March 16, Vincent 113
Robert Gulliver
Chern-Gauss-Bonnet, Chern-Lashof and minimal submanifolds
Abstract: Let Gamma be a compact n-1 dimensional submanifold of Euclidean space R^d; we are interested in immersed minimal submanifolds Sigma, or stationary n-rectifiable integral currents, having Gamma as boundary. Assume n is even. If Gamma lies in the boundary of a bounded, strictly convex open set of R^d, then the density of Sigma at any point is bounded by a constant times the total curvature of Gamma. The proof is based on Chern誷 1944 Gauss-Bonnet formula. The version of total curvature is related to, but stronger than, the version considered by Chern and Lashof. This is joint work with Jaigyoung Choe.

9:30, March 17, Vincent 113
Ronald Fintushel
4-manifolds with b^+ = 1

11:00, March 17, Vincent 113
Michael Usher
Floer homologies for fibered 3-manifolds

2:00, March 17, Vincent 113
Yi Hu
Topology aspects of Chow quotients

9:30, March 18, Vincent 113
Mikio Furuta
10/8 type inequality for spin 4-manifolds with $b_1>0$

11:00, March 18, Vincent 113
Bo Dai
Soliton solutions of the self-dual Yang-Mills equation on $R^{2,2}$
Abstract. The self-dual Yang-Mills equation on $R^{2,2}$ has a Lax pair and is an integrable system. We apply techniques from integrable systems to construct explicit self-dual $U(n)$ connections whose parallel frames are rational in the spectral parameter. I will also talk about results of Uhlenbeck, Terng and myself on some integrable systems coming from dimension reductions of the self-dual Yang-Mills equation, such as the modified $2+1$ chiral model, the 2D chiral model, and the $1+1$ wave maps (This is a joint work with Chuu-Lian Terng).

9:30, March 19, Vincent 113
John Loftin
Singular Semi-Flat Calabi-Yau Metrics on $S^n$

11:00, March 19, Vincent 113
Spiro Karigiannis
The Moduli Space of G_2 Metrics
Abstract: Manifolds with G_2 holonomy have many features in common with Calabi-Yau threefolds. Their local moduli spaces are also unobstructed, and are diffeomorphic to an open subset of a vector space. The proof of this fact is due to Joyce and Hitchin and lies on an implicit function theorem argument. In contrast, the Tian-Todorov theorem gives a much more concrete construction of the local Calabi-Yau moduli space. I will discuss ongoing joint work with Naichung Conan Leung in obtaining a similar explicit description of the G_2 moduli space.

10:00, March 20, Vincent 113
Jaeyouk Lee
Symplectic Grassmannian Geometry

10:00, March 21, Vincent 203B
Xiaowei Wang
Chern number inequality and convexity of moment map

10:00, March 22, Vincent 203B
Tian-Jun Li
Diffeomorphism groups of rational and ruled surfaces