
September 26
Valentino Tosatti  εregularity theorems  Reference

October 3
Ben Weinkove  The uniform estimate in the CalabiYau theorem  Reference

October 10
Jian Song (Rutgers)  The Ricci flow on the sphere with marked points  Reference

October 17
Tao Zheng  Gradient estimates for harmonic functions on manifolds  Reference

October 24
Xiaokui Yang  A numerical characterization of the Kähler cone  Reference

October 31
Greg Edwards  Perelman's work on the KählerRicci flow  Reference

November 7
Shouwen Fang  The LiYau Harnack inequality  Reference

November 14
Xiaokui Yang  A numerical characterization of the Kähler cone  Reference

November 21
Tristan Collins (Harvard)  C^{2,α} estimates for fully nonlinear equations  Reference

January 9
Valentino Tosatti  Kołodziej's uniform estimate in the CalabiYau theorem  Reference

January 16  Special time: 4:10pm
Valentino Tosatti  Kołodziej's uniform estimate in the CalabiYau theorem  Reference

January 23
Shouwen Fang  Perelman's W functional and no local collapsing  Reference

January 30
Tao Zheng  The Schwarz Lemma  Reference

February 6
Valentino Tosatti  Hörmander's uniform integrability of plurisubharmonic functions

February 13
Aaron Peterson  CarnotCarathéodory metrics

February 20
Tamás Darvas (Maryland)  Geometry of the space of Kähler metrics  Abstract
Suppose (X,ω) is a compact connected Kähler manifold. We
denote by H the set of Kähler metrics that are cohomologous to ω.
This set is an infinite dimensional Fréchet manifold with a natural
Riemannian structure, investigated by Mabuchi and Donaldson independently
in connection with existence and uniqueness of special Kähler metrics. In
the first part of the talk we survey the main ideas behind this intriguing
geometric phenomenon. In the second part of the talk we will explore recent
developments related to the path length metric structure of H and their
applications.

February 27
Greg Edwards  The conical KählerRicci flow  Reference

March 6
Valentino Tosatti  Singular metrics on holomorphic line bundles  Reference

March 12  Special date, time and location: 4.00pm, Lunt 107
Valentino Tosatti  Singular metrics on holomorphic line bundles  Reference

April 3  Special time and location: 1.00pm, Annenberg G29
Valentino Tosatti  Singular metrics on holomorphic line bundles  Reference

April 10
Xiaolan Nie (Ohio State)  Weak solutions of the ChernRicci flow  Abstract
We will talk about weak solutions of the ChernRicci flow on compact Hermitian manifolds. We will also discuss the behavior of the flow on complex surfaces. In particular, if the flow is noncollapsing in finite time, it is conjectured that it contracts exceptional curves and continue in a unique way on a new surface. We will discuss some related results on this.

April 16  Special date, time and location: 4.00pm, Lunt 107
Dror Varolin (Stony Brook)  Two Bergmantype interpolation problems on finite Riemann surfaces  Abstract
Let X be an open Riemann surface with a Hermitian metric and a weight function (i.e. nontrivial metric for the trivial line bundle). Given a
closed discrete subset G in X, the above data defines a Bergman space on X and a Hilbert space on G (in a standard way). We say that G is an
interpolation set if the restriction map from the Bergman space on X to the Hilbert space on G is
surjective. The interpolation problem consists in characterizing all interpolation sets.
When X is the complement of a finite set in a compact Riemann surface
(i.e., a compact Riemann surface with some finite number of punctures), the metric g
is flat outside some compact subset of X, and the curvature of the weight satisfies
certain positivity and boundedness conditions, we give a complete solution to the
interpolation problem.
We then turn our attention to more general bordered Riemann surfaces with
finitely many punctures. We equip these with the unique metric of constant negative
curvature 4, and point out that the same Bergman interpolation problem discussed above does not
have a reasonable solution. We therefore modify the problem so that it doesn't change in the
asymptotically flat case, but has a reasonable solution in the hyperbolic case. Finally, we
give a complete characterization of interpolation sets for this modified problem.

April 24
Lei Wu  Variations of Hodge structures and Hodge metrics  Reference 1 2

May 1
Wenshuai Jiang  Convexity of the Kenergy  Reference

May 8
Lei Wu  Variations of Hodge structures and Hodge metrics  Reference 1 2

May 15
Wenshuai Jiang  Convexity of the Kenergy  Reference