Where: Kirwan Hall 1308

Speaker: Ben Weinkove (Northwestern) -

Abstract: Yau's Theorem on the complex Monge-Ampere equation shows that one can prescribe the volume form of a Kahler metric on a compact Kahler manifold. I will describe extensions of this result to non-Kahler settings. In each case, a Monge-Ampere type equation is used to prescribe the volume form of a special metric on a complex or almost complex manifold. This talk is based on joint works with Tosatti, Szekelyhidi and Chu.

Where: JHU

Speaker: Hao Xu (University of Pittsburgh) -

Abstract: The asymptotic expansion for the Bergman kernel has important applications in complex analysis. Short-time asymptotic expansion of the heat kernel played an important role in spectral geometry. We will present our work on Feynman diagram formulas for the coefficients in the asymptotic expansion of Bergman and heat kernels on Kahler manifolds and their applications.

Where: Kirwan Hall 1308

Speaker: Mu-Tao Wang (Columbia) -

Abstract: I shall present some new long time existence and convergence theorems of Lagrangian curvature flows in cotangent bundles of spheres with either the canonical metric or the Stenzel (Calabi-Yau) metric. The talk will be based on joint work with Knut Smoczyk and Mao-Pei Tsui, and joint work with Chung-Jun Tsai.

Where: Maryland Hall 114(JHU)

Speaker: Duong Phong (Columbia) -

Abstract: In the mid 1980s, C. Hull and A. Strominger proposed a system of equations for supersymmetric vacua of superstrings, which are generalizations with torsion of the Calabi-Yau condition proposed shortly before by P. Candelas, G. Horowitz, A. Strominger, and E. Witten. As such, they are also of interest from the point of view of non-Kahler geometry and partial differential equations. We introduce a flow, called the Anomaly Flow, whose fixed points would provide solutions of the Hull-Strominger system. We provide criteria for the long-time existence of the flow, and show that it can recapture the celebrated solution found in 2006 by J. Fu and S.T. Yau on toric fibrations over K3 surfaces. This last result may be of particular interest in the theory of non-linear partial differential equations, as the corresponding parabolic scalar equation is not concave. This is joint work with S. Picard and X.W. Zhang.

Where: Ames 218 (Johns Hopkins)

Speaker: Xiaofeng Sun (Lehigh) -

Abstract: In this talk we will describe a new necessary and sufficient condition on the existence of KE metrics on all small deformation of a Fano KE manifold with nontrivial automorphism group. We will also describe a canonical extension of pluri-anticanonical forms from a Fano KE manifold to its small deformations which leads to simultaneous embedding of a family of Fano manifolds into projective spaces with effective control. We will also discuss a construction of plurisubharmonic functions on Teichmuller spaces of KE manifolds of general type by using energy of equivariant harmonic maps.

Where: Ames 218(JHU)

Speaker: Xiaojun Huang (Rutgers) -

Where: Kirwan Hall 1308

Speaker: Mattias Jonsson ((University of Michigan)) -

Abstract: I will present joint work with Robert Berman and Sebastien Boucksom, on a new proof of a uniform version of the Yau-Tian-Donaldson conjecture for Fano manifolds with finite automorphism group. Our approach does not involve the continuity method or Cheeger-Colding-Tian theory. Instead, the proof is variational and uses pluripotential theory and certain non-Archimedean considerations.