
September 8
Organizational Meeting
Valentino Tosatti  Nonsmooth geodesics
in the space of Kähler metrics
 Reference

September 15
J.J. Kohn (Princeton)  Hypoellipticity and loss of derivatives  Reference

September 22
Jian Song  Bounding scalar curvature for global solutions of
the KählerRicci flow 
References 1 2 3

September 29
Donovan McFeron  The Mabuchi metric and the KählerRicci flow  Reference

October 6
Sławomir Dinew  MoserTrudinger type inequalities for complex MongeAmpère operators and a conjecture of Aubin  Reference

October 13
Valentino Tosatti  Volume estimates for KählerEinstein manifolds
 Reference

October 27
Xiaowei Wang  bstability and blowups  Reference
November 3
Ovidiu Munteanu  Bounds on volume growth of geodesic balls under Ricci flow
 References 1 2

November 10
Tristan Collins  The transverse entropy functional and the SasakiRicci flow
 Reference

November 17
Adam Jacob  The YangMills flow and the AtiyahBott formula on compact Kähler manifolds  Reference

December 1
Xiaowei Wang  bstability and blowups II  Reference

December 8
Tristan Collins  The ACC Conjecture for log canonical thresholds  References 1
2

January 26
Organizational Meeting 2:40pm3:00pm
Frederick T.H. Fong (Stanford)  Collapsing Behavior of the KählerRicci flow and its Singularity Analysis
 References 1 2  Abstract
In this talk, I will discuss my recent works on the collapsing behavior of the KählerRicci flow. The first work studies the KählerRicci flow on P^{1}bundles over KählerEinstein manifolds. We proved that if the initial Kähler metric is constructed by the Calabi's Ansatz and is in the suitable Kähler class, the flow must develop Type I singularity and the singularity model is P^{1} X C^{n}. It is an extension of SongWeinkove's work on Hirzebruch surfaces. The second work discusses the collapsing behavior in a more general setting without any symmetry assumption. We showed that if
the limiting Kähler class of the flow is given by a holomorphic submersion and the Ricci curvature is uniformly bounded from above with respect to the initial metric, then the fibers will collapse in an optimal rate, i.e. diam~(Tt)^{1/2}. It gives a partial affirmative answer to a conjecture stated in SongSzekelyhidiWeinkove's work on projective bundles.

February 2
Ben Weinkove (UCSD)  The evolution of a Hermitian metric by its ChernRicci form
 Reference  Abstract
I will discuss the evolution of a Hermitian metric on a
compact complex manifold by its ChernRicci form. This is an evolution
equation first studied by M. Gill, and coincides with the KählerRicci
flow if the initial metric is Kähler. I will describe the maximal
existence time for the flow in terms of the initial data. I will
discuss the behavior of the flow on complex surfaces when the initial
metric is Gauduchon, on complex manifolds with negative first Chern
class, and on some Hopf manifolds. This is a joint work with
Valentino Tosatti.

February 9
Yu Wang  C^{2,α} regularity for the complex MongeAmpère equation  Reference

February 16
Tristan Collins  Affine Kstability

February 23
Sławomir Dinew  Hölder continuous solutions to MongeAmpère equations  Reference

March 1
Valentino Tosatti  Strominger's system  Reference

March 8
Valentino Tosatti  Strominger's system II  Reference

March 22
Jian Song  Formtype CalabiYau equations  References 1 2

March 29
Xiaowei Wang  Kähler metrics with cone singularities along a divisor  Reference

April 5
Yu Wang  Integrability exponents of plurisubharmonic functions  Reference

April 12
Michael Siepmann (ETH Zürich)  Ricci Flat Cones and expanding (Kähler) Ricci Solitons  Abstract
We consider the question whether a Ricci flat cone admits a smooth Ricci flow coming out of it.
After some general observations about such Ricci flows we study the MongeAmpère equation associated to the (expanding) soliton equation on Kähler manifolds with one asymptotically Ricci flat conical end. Solutions will provide examples of possibly nonrotationally symmetric expanding Kähler Ricci solitons. We will also sketch an approach to construct explicit nonrotationally symmetric expanders which flow out of Ricci flat cones.

April 16  Special Date  4.30pm to 5.30pm in Math 507
Martine Klughertz (Toulouse)  The holonomy group at infinity of the Painlevé VI Equation  Abstract
It will be proven that the holonomy group at infinity of the Painlevé VI equation is virtually commutative.
It is is related to differential Galois theory and motivated by the study of nonintegrability of
Hamiltonian systems by ZiglinMoralesRamisSimo. (joint work with Bassem ben Hamed and Lubomir Gavrilov).

April 20
Special Day on Complex Geometry and PDE
 Details

May 3
Dan Rubin  The Willmore flow with small initial energy  Reference