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Graduate Workshop on Kahler Geometry, June 24 – July 5, 2013

 

Workshop in Kahler Geometry-Summer 2013

Recently there have been spectacular developments in Kahler geometry which cut across a wide variety of mathematical fields ranging from the analysis of PDE’s to Algebraic Geometry. The purpose of this workshop is to introduce graduate students and young researchers to some of these developments. The workshop will be organized by Xiuxiong Chen, Sir Simon Donaldson, Paul Gauduchon, and Sean Timothy Paul.   More specifically, the goal of the program is to lay the groundwork for further advances in the following subjects:

(1) The existence of Canonical metrics on Kahler Manifolds (Kahler Einstein cone metrics, Constant Scalar curvature metrics, and Extremal metrics).

(2) The alpha invariant, log canonical threshold, and stability conditions from algebraic geometry.

(3) Geometric Flows (Kahler Ricci and Calabi flows).

(4) The theory of the Complex Monge Ampere equation.

The first part of the workshop will consist of short courses delivered by the organizers and other senior mathematicians in residence. These lectures will be followed by student seminars which expand on the topics covered in the minicourses. The emphasis will be on understanding Yau’s solution to the Calabi Conjecture (and its conical analogue) , Geometric Invariant Theory and Kahler energies, and the basic ideas behind Gromov Haussdorf convergence of manifolds with specific geometric constraints .

Accepted applicants will be provided breakfast, lunch and local accommodations.

List of Faculty Lecturers: Simon Donaldson, Paul Gauduchon, Weiyong He, Hongnian Huang, Claude LeBrun, Jesus Martinez-Garcia, Sean Paul, Ioana Suvaina, Dror Varolin, and Ben Weinkove

Download Talk Schedule- 1st WeekDownload Talk Schedule- 2nd Week

Attendee ListDownload Poster

Graduate Workshop on Kahler Geometry Schedule

Time Title Presenters  Video
 9:00am Introduction to Differential geometry on toric varieties- 1 hr Simon Donaldson video
10:30am Curvature Functionals, Kähler Metrics, and the Geometry of 4-Manifolds- 1.5 hr Claude LeBrun video
12:00pm Lunch Simons Center Cafe
 1:30pm Introduction to Calabi extremal Kaehler metrics- 2hr Paul Gauduchon video
 3:30pm Tea Time Simons Center 515
 4:00pm Monge-Ampere equations on complex manifolds- 1 hr Ben Weinkove video


Time Title Presenters  Video
 9:00am Introduction to Differential geometry on toric varieties- 1 hr Simon Donaldson video
10:30am Stability notions in Kahler and Algebraic Geometry- 1 hr Sean Paul video
12:00pm Lunch Simons Center Cafe
 1:30pm Introduction to Calabi extremal Kaehler metrics- 2hr Paul Gauduchon video
 3:30pm Tea Time Simons Center 515
 4:00pm On the space of Kahler potentials- 1hr Weiyong He video

Time Title Presenters  Video
 9:00am Introduction to Calabi extremal Kaehler metrics- 2 hr Paul Gauduchon video
11:30am  Curvature Functionals, Kähler Metrics, and the Geometry of 4-Manifolds- 1.5 hr Claude LeBrun video
 1:00pm Lunch Simons Center Cafe
 3:30pm Tea Time Simons Center 515


Time Title Presenters  Video
 9:00am A splitting theorem on toric varieties- 1 hr Hongnian Huang video
10:30am 1.5 hr Student Talks talk 1
talk 2
12:00pm Lunch Simons Center Cafe
 1:30pm Introduction to Calabi extremal Kaehler metrics- 2 hr Paul Gauduchon video
 3:30pm Tea Time Simons Center 515
 4:00pm Hormander’s Theorem and applications- 1 hr Dror Varolin video
 6:00pm Workshop Banquet Simons Center Cafe

 


Time Title Presenters  Video
 9:00am The classification of ALE Ricci flat Kahler surfaces- 1 hr Ioana Suvaina video
10:30am Curvature Functionals, Kähler Metrics, and the Geometry of 4-Manifolds- 1.5 hr Claude LeBrun video
12:00pm Lunch Simons Center Cafe
 1:30pm Introduction to Calabi extremal Kaehler metrics- 2 hr Paul Gauduchon video
 3:30pm Tea Time Simons Center 515
 4:00pm Ohsawa-Takegoshi Extension Theorem- 1 hr Dror Varolin video


Time Title Presenters  Video
 9:00am Stability notions in Kahler and Algebraic Geometry- 1 hr Sean Paul video
10:30am Curvature Functionals, Kähler Metrics, and the Geometry of 4-Manifolds- 1.5 hr Claude LeBrun video
12:00pm Lunch Simons Center Cafe
 2:00pm Invariance of Plurigenera- 1 hr Dror Varolin video
 3:30pm Tea Time Simons Center 515
 4:00pm Kahler-Einstein metrics and Algebraic Geometry. Computing Tian’s alpha-invariant.- 1hr Jesus Martinez-Garcia video

Time Title Presenters  Video
 9:00am Stability notions in Kahler and Algebraic Geometry- 2 hr Sean Paul video
11:30am 1 hr Student Talks talk 2
talk 3
12:30pm Lunch Simons Center Cafe
 2:00pm Basics of Bergman kernels- 1 hr Dror Varolin video
 3:30pm Tea Time Simons Center 515
 4:00pm Kahler-Einstein metrics and Algebraic Geometry. Computing Tian’s alpha-invariant.- 1hr Jesus Martinez-Garcia video

Time Title Presenters  Video
 9:00am Stability notions in Kahler and Algebraic Geometry- 2 hr Sean Paul video
11:30am Curvature Functionals, Kähler Metrics, and the Geometry of 4-Manifolds- 1.5 hr Claude LeBrun video
 1:00pm Lunch Simons Center Cafe
 2:30pm The openness conjecture- 1 hr Dror Varolin video
 3:30pm Tea Time Simons Center 515
 4:00pm Kahler-Einstein metrics and Algebraic Geometry. Computing Tian’s alpha-invariant.- 1hr Jesus Martinez-Garcia video

Time Title Presenters  Video
All day Simons Center is closed due to US holiday

Time Title Presenters  Video
All day Informal day