
September 10
Phong  Organizational Meeting

September 17
Jian Song  The KählerRicci flow on complex surfaces  Reference

September 24
Valentino Tosatti  Lower boundedness of the Kenergy on deformations of the Mukai threefold I  Reference

October 1
Valentino Tosatti  Lower boundedness of the Kenergy on deformations of the Mukai threefold II  Reference

October 8
Gábor Székelyhidi  Holomorphic discs and the homogeneous complex MongeAmpère equation
 Reference

October 15
Jacob Sturm  Convergence of Riemannian Manifolds I  Reference

October 29
Jacob Sturm  Convergence of Riemannian Manifolds II  Reference

November 5
Valentino Tosatti  Quantization of the space of Kähler metrics  References 1 2

November 12
TienCuong Dinh  Exponential estimates for plurisubharmonic
functions and applications to dynamics  Reference

November 19
Gábor Székelyhidi  Kstability of constant scalar curvature Kähler manifolds  Reference

December 10
Valentino Tosatti  KählerEinstein metrics on Fano surfaces I  Reference

January 28
Valentino Tosatti  KählerEinstein metrics on Fano surfaces II  Reference

February 4
Gábor Székelyhidi  Okounkov bodies and test configurations  References 1 2

February 11
Jian Song  Regularity of plurisubharmonic upper envelopes in big cohomology classes
 Reference

February 18
Jacob Sturm  A variational approach to complex MongeAmpère equations  Reference

February 25
Phong  Convergence properties of the YangMills flow on Kähler surfaces  References 1 2 3 4 5

March 4
Gábor Székelyhidi  The Bernstein problem for affine maximal hypersurfaces  Reference

March 11
Valentino Tosatti  Harmonic maps and rectifiability  Reference

March 25
Ovidiu Munteanu  Regularity of weakly harmonic maps  References 1 2
3

April 1
Nam Q. Le  The affine Plateau problem  Reference

April 8
Ben Weinkove (UC San Diego)  Contracting exceptional divisors by the KählerRicci flow  Reference  Abstract
We give a criterion under which a solution g(t) of the KählerRicci flow
contracts exceptional divisors on compact manifold and can be uniquely
continued on a new manifold. This is a joint work with Jian Song.

April 15
Vincent Guedj (Marseille)  Viscosity solutions to degenerate complex MongeAmpère equations  Abstract
Degenerate complex MongeAmpère equations on compact
Kähler manifolds have been recently intensively studied using tools
from pluripotential theory. We develop an alternative approach based on
the concept of viscosity solutions.
This approach works only for a rather restricted type of degenerate
complex MongeAmpère equations. Nevertheless, we prove that the local
potentials of the singular KählerEinstein metrics constructed
previously by the authors are continuous plurisubharmonic functions.
They were previously known to be locally bounded.
Another application is a lower order construction with a C^{0}estimate
of the solution to the Calabi conjecture which does not use Yau's
celebrated theorem. This is joint work with P.Eyssidieux and A.Zeriahi.

April 22
Sławomir Dinew (Jagiellonian University)  Hölder regularity for complex MongeAmpère equations  Abstract
In geometric analysis many arguments rely on a suitable regularity theory for the
analyzed differential equations. Similarly to the solution of the Calabi conjecture often
deriving suitable a priori estimates is in fact the heart of the matter.
In the talk a regularity result for the complex MongeAmpère equation will be presented.
We will prove that any C^{1,1} smooth plurisubharmonic solution u to the problem
det(u_{ij̄}) = f
with f strictly positive and Hölder continuous has in fact Hölder continuous second
derivatives. For smoother f this follows form the classical EvansKrylov theory yet in
our case it cannot be applied directly. Instead we shall follow closely an idea of XuJia
Wang.
Finally we shall discus how this particular regularity result can be used to justify an
argument in the proof of uniqueness of metrics of constant scalar curvature by Chen and
Tian.
Yuan Yuan (Rutgers)  KählerRicci flow on singular CalabiYau varieties

April 29
Adam Jacob  Nonabelian Hodge Theory  References 1 2 3

May 6
Jacob Sturm  The structure of spaces with Ricci curvature bounded below  Part I  References 1 2
Jacob Sturm  The structure of spaces with Ricci curvature bounded below  Part II  References 1 2

May 13
Valentino Tosatti  Convergence of Einstein manifolds  References 1
2

May 20
Jacopo Stoppa (Cambridge)  DonaldsonThomas invariants and hyperkähler metrics  Reference  Abstract
I will briefly introduce DonaldsonThomas invariants counting semistable sheaves on a CalabiYau threefold. I will then try to turn this into a differential geometry seminar, relying on the work of Gaiotto, Moore and Nietzke that connects DT invariants to some special hyperkähler metrics. I aim at pointing out one analogy between their metrics
and some results I wrote down in this preprint.