
September 24
Valentino Tosatti  An introduction to compensated compactness

October 1
Jianchun Chu  C^{2,α} estimates for some nonlinear elliptic equations of second order in geometry  Abstract
Recently, TosattiWangWeinkoveYang established C^{2,α}
estimates for solutions of some nonlinear elliptic equations in complex
geometry, assuming a bound on the Laplacian of the solution. On the basis
of their work, we can lift α to the optimal Hölder exponent.

October 8
Teng Fei (MIT)  Some new solutions to the Strominger system  Abstract
The Strominger system is a system of PDEs derived by Strominger in his study of compactification of heterotic strings with torsion. It can be thought of as a generalization of Ricciflat metrics on nonKähler CalabiYau 3folds. We present some new solutions to the Strominger system on a class of noncompact 3folds constructed by twistor technique. These manifolds include the resolved conifold Tot(O(1,1)>P^{1}) as a special case.

October 15
Ben Weinkove  Twopoint maximum principles

October 22
Valentino Tosatti  An introduction to compensated compactness II

November 5
Greg Edwards  The KählerRicci flow on elliptic surfaces  Reference

November 11  Special date, time and location: 4.00pm, Lunt 105
Daniele Angella (Florence)  Cohomologies and special metrics for nonKähler manifolds  Abstract
We present some results on BottChern cohomology of compact complex
manifolds and on the existence of special metrics on nonKähler
manifolds. The ChernRicci form of a Hermitian metric representing a
class in BottChern cohomology, special geometry is in a sense related
to cohomological properties. More precisely, we will investigate an
analogue of the Yamabe problem for Hermitian metrics with Chern
connection. (Joint works with Adriano Tomassini, Simone Calamai,
Cristiano Spotti, Nicoletta Tardini.)

December 10
Guillaume RoyFortin  L^{q} norms and nodal sets of Laplace eigenfunctions  Abstract
We will discuss a recent result that exhibits a relation between the
average local growth of a Laplace eigenfunction on a compact, smooth
Riemannian surface and the global size of its nodal (zero) set. More
precisely, we provide a lower and an upper bound for the Hausdorff
measure of the nodal set in terms of the average of the growth exponents
of an eigenfunction on disks of small radius. Combined with Yau's
conjecture
and the work of DonnellyFefferman, the result implies that the average
local growth of eigenfunctions on an analytic manifold with analytic
metric is bounded by constants in the semiclassical limit.

January 22
Greg Edwards  The KählerRicci flow on elliptic surfaces  Reference

January 29
Ben Weinkove  The Fundamental Gap Conjecture  References 1 2

February 5
Ben Weinkove  The Fundamental Gap Conjecture  References 1 2

February 12
Morgan Sherman (Cal Poly)  An explicit construction of extremal metrics on a ruled complex surface

February 19
Steve Zelditch  Partial Bergman kernel asymptotics  Reference

February 26
Jianchun Chu  Regularity of psh envelopes  Reference

April 1
Valentino Tosatti  Pluripolar graphs are holomorphic  Reference

April 14
Jianchun Chu  Complex MongeAmpère equations with right hand side in L^{p}  Reference

April 21
Yu Wang  kRectifiability of a measure in R^{n} under
a Reifenbergtype condition

April 28
Greg Edwards  The Ricci flow on the sphere with marked points  References 1 2

May 6  Special date and time: 4.00pm, Lunt 107
Oran Gannot (Berkeley)  Quasinormal modes for KerrAdS spacetimes  Abstract
KerrAdS spacetimes are rotating black hole solutions to the Einstein equations with negative cosmological constant. Recently, timeperiodic approximate solutions (quasimodes) for the KleinGordon equation were constructed on these spacetimes by HolzegelSmulevici as a way of proving lower bounds on uniform energy decay. I will show how these quasimodes can be used to exhibit sequences of quasinormal modes (outgoing waves) at complex frequencies which converge exponentially to the real axis.

May 11  Special date, time and location: 1.00pm, Lunt 102
Mihai Păun (KIAS)  Pretalk: Metrics on relative canonical bundles

May 11  Special date, time and location: 4.00pm, Lunt 105
Mihai Păun (KIAS)  Psh variation of twisted KählerEinstein metrics and applications

May 12
Guillaume RoyFortin  Yau's conjecture and the recent work of Logunov/Malinnikova  Abstract
We review the status of Yau's conjecture on nodal sets of
Laplace eigenfunctions in light of the various new results claimed by
Logunov and Malinnikova in 3 preprints that were made public on Tuesday.
We present their proof of an improvement for the upper bound of the length
of the nodal set on surfaces.

May 19
Zahra Sinaei  Convergence of harmonic maps  Abstract
In this talk I will present a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds. The sequence of manifolds will be considered in the space of compact ndimensional Riemannian manifolds with bounded sectional curvature and bounded diameter, equipped with measured GromovHausdorff topology.