Symplectic and Differential Geometry Seminar
   Vanderbilt University
   Fall 2012

   Organizers:  Basak Gurel and Ioana Suvaina

   Mondays, 4:10-5:00pm in SC 1308 (unless otherwise noted) RESCHEDULED FROM 3:10-4:00pm, in SC 1310, starting Oct 29th.

   Related seminars also announced.

Monday, September 3rd, 2012,

Speaker: Mehdi Lejmi, University of Minnesota

Title: Deformations of non integrable hermitian-Einstein metrics

Abstract:  Previously, we studied deformations of extremal almost-kahler metrics starting from an extremal
(integrable) kahler metric. In this talk, we explore deformations of these metrics but starting from
(not necessarily integrable) extremal almost-kahler metric. We restrict our attention to non integrable
hermitian-Einstein metrics and give some explicit examples.

 

Monday, September 17th, 

Speaker: Marcelo Disconzi, Vanderbilt University

Title: Compactness results for the Yamabe problem, I

Abstract: There is going to be a sequence of three lectures.
A detailed abstract is attached in .pdf format here.


Monday, September 24th, 

Speaker: Marcelo Disconzi, Vanderbilt University

Title: Compactness results for the Yamabe problem, II

                  Abstract:  abstract for the lectures series can be found here.


Monday, October 8th, 

Speaker: Marcelo Disconzi, Vanderbilt University

Title: Compactness results for the Yamabe problem, III

                  Abstract: abstract for the lectures series can be found here.


Monday, October 15th, 

Speaker: Caner Koca, Vanderbilt University

Title: Positively Curved Einstein Manifolds in Dimension Four, I

                  Abstract: The general theme of this series of talks will be "four-dimensional
            Einstein Manifolds".

            In the first talk we will review some of the important facts about the topology and geometry of 4-manifolds.
            In particular we will see that the dimension four is crucial for different special reasons. One reason is that the
            theory of Einstein metrics is relatively well-understood for complex surfaces. For this, we will also recall the
            basics of complex geometry and Kähler manifolds. The whole presentation will be supported by lots of examples.

            Our goal in this series is to present the proof of the following uniqueness theorem: In dimension 4, the only positively
            curved Einstein metric compatible with a complex structure is the Fubini-Study metric on the complex projective plane.

            The first talk is introductory and accessible to graduate students.


Monday, October 29th, RESCHEDULED FROM 3:10-4:00pm, in SC 1310

Speaker: Caner Koca, Vanderbilt University

Title: Positively Curved Einstein Manifolds in Dimension Four, I (rescheduled)

                  Abstract: the seminar on Monday Oct 15th was cancelled. We resume on Monday 29th, at the new location, and time.



                   
 

Wednesday, November 14th, from 3:10-4:00pm, in SC 1310, RESCHEDULED

Speaker: Caner Koca, Vanderbilt University

Title: Positively Curved Einstein Manifolds in Dimension Four, II 

                  Abstract: There are only two known examples of positively curved compact (orientable) Einstein 4-manifolds:
                The round metric on the 4-sphere, and the Fubini-Study submersion metric on the complex projective plane. It is
                an open question whether or not this is the complete list. In this talk, we will prove that if we in addition assume
                that the metric is compatible with a complex structure on the manifold, then it has to be the Fubini-Study metric.



Old Seminar Web-Pages: Fall 2009, Fall 2010, Spring 2011, Fall 2011, Spring 2012