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September 26
Valentino Tosatti - ε-regularity theorems - Reference
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October 3
Ben Weinkove - The uniform estimate in the Calabi-Yau theorem - Reference
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October 10
Jian Song (Rutgers) - The Ricci flow on the sphere with marked points - Reference
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October 17
Tao Zheng - Gradient estimates for harmonic functions on manifolds - Reference
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October 24
Xiaokui Yang - A numerical characterization of the Kähler cone - Reference
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October 31
Greg Edwards - Perelman's work on the Kähler-Ricci flow - Reference
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November 7
Shouwen Fang - The Li-Yau Harnack inequality - Reference
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November 14
Xiaokui Yang - A numerical characterization of the Kähler cone - Reference
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November 21
Tristan Collins (Harvard) - C2,α estimates for fully nonlinear equations - Reference
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January 9
Valentino Tosatti - Kołodziej's uniform estimate in the Calabi-Yau theorem - Reference
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January 16 - Special time: 4:10pm
Valentino Tosatti - Kołodziej's uniform estimate in the Calabi-Yau theorem - Reference
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January 23
Shouwen Fang - Perelman's W functional and no local collapsing - Reference
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January 30
Tao Zheng - The Schwarz Lemma - Reference
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February 6
Valentino Tosatti - Hörmander's uniform integrability of plurisubharmonic functions
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February 13
Aaron Peterson - Carnot-Carathéodory metrics
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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.
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February 27
Greg Edwards - The conical Kähler-Ricci flow - Reference
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March 6
Valentino Tosatti - Singular metrics on holomorphic line bundles - Reference
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March 12 - Special date, time and location: 4.00pm, Lunt 107
Valentino Tosatti - Singular metrics on holomorphic line bundles - Reference
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April 3 - Special time and location: 1.00pm, Annenberg G29
Valentino Tosatti - Singular metrics on holomorphic line bundles - Reference
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April 10
Xiaolan Nie (Ohio State) - Weak solutions of the Chern-Ricci flow - Abstract
We will talk about weak solutions of the Chern-Ricci flow on compact Hermitian manifolds. We will also discuss the behavior of the flow on complex surfaces. In particular, if the flow is non-collapsing 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.
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April 16 - Special date, time and location: 4.00pm, Lunt 107
Dror Varolin (Stony Brook) - Two Bergman-type interpolation problems on finite Riemann surfaces - Abstract
Let X be an open Riemann surface with a Hermitian metric and a weight function (i.e. non-trivial 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.
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April 24
Lei Wu - Variations of Hodge structures and Hodge metrics - Reference 1 2
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May 1
Wenshuai Jiang - Convexity of the K-energy - Reference
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May 8
Lei Wu - Variations of Hodge structures and Hodge metrics - Reference 1 2
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May 15
Wenshuai Jiang - Convexity of the K-energy - Reference