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September 24
Valentino Tosatti - An introduction to compensated compactness
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October 1
Jianchun Chu - C2,α estimates for some nonlinear elliptic equations of second order in geometry - Abstract
Recently, Tosatti-Wang-Weinkove-Yang established C2,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.
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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 Ricci-flat metrics on non-Kähler Calabi-Yau 3-folds. We present some new solutions to the Strominger system on a class of noncompact 3-folds constructed by twistor technique. These manifolds include the resolved conifold Tot(O(-1,-1)->P1) as a special case.
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October 15
Ben Weinkove - Two-point maximum principles
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October 22
Valentino Tosatti - An introduction to compensated compactness II
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November 5
Greg Edwards - The Kähler-Ricci flow on elliptic surfaces - Reference
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November 11 - Special date, time and location: 4.00pm, Lunt 105
Daniele Angella (Florence) - Cohomologies and special metrics for non-Kähler manifolds - Abstract
We present some results on Bott-Chern cohomology of compact complex
manifolds and on the existence of special metrics on non-Kähler
manifolds. The Chern-Ricci form of a Hermitian metric representing a
class in Bott-Chern 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.)
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December 10
Guillaume Roy-Fortin - Lq 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 Donnelly-Fefferman, the result implies that the average
local growth of eigenfunctions on an analytic manifold with analytic
metric is bounded by constants in the semi-classical limit.
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January 22
Greg Edwards - The Kähler-Ricci flow on elliptic surfaces - Reference
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January 29
Ben Weinkove - The Fundamental Gap Conjecture - References 1 2
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February 5
Ben Weinkove - The Fundamental Gap Conjecture - References 1 2
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February 12
Morgan Sherman (Cal Poly) - An explicit construction of extremal metrics on a ruled complex surface
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February 19
Steve Zelditch - Partial Bergman kernel asymptotics - Reference
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February 26
Jianchun Chu - Regularity of psh envelopes - Reference
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April 1
Valentino Tosatti - Pluripolar graphs are holomorphic - Reference
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April 14
Jianchun Chu - Complex Monge-Ampère equations with right hand side in Lp - Reference
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April 21
Yu Wang - k-Rectifiability of a measure in Rn under
a Reifenberg-type condition
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April 28
Greg Edwards - The Ricci flow on the sphere with marked points - References 1 2
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May 6 - Special date and time: 4.00pm, Lunt 107
Oran Gannot (Berkeley) - Quasinormal modes for Kerr-AdS spacetimes - Abstract
Kerr-AdS spacetimes are rotating black hole solutions to the Einstein equations with negative cosmological constant. Recently, time-periodic approximate solutions (quasimodes) for the Klein-Gordon equation were constructed on these spacetimes by Holzegel-Smulevici 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.
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May 11 - Special date, time and location: 1.00pm, Lunt 102
Mihai Păun (KIAS) - Pretalk: Metrics on relative canonical bundles
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May 11 - Special date, time and location: 4.00pm, Lunt 105
Mihai Păun (KIAS) - Psh variation of twisted Kähler-Einstein metrics and applications
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May 12
Guillaume Roy-Fortin - 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.
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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 n-dimensional Riemannian manifolds with bounded sectional curvature and bounded diameter, equipped with measured Gromov-Hausdorff topology.