Symplectic and Differential Geometry Seminar
Vanderbilt University
Fall 2010

Organizers:  Basak Gurel and Ioana Suvaina

Tuesdays, 1:10 - 2:00 pm in SC 1310 (unless otherwise noted)

Related seminars also announced.

 

Tuesday, September 14 2010

Speaker:  Rares Rasdeaconu, Vanderbilt University

Title: Relative Open Gromov-Witten Invariants II

Abstract: We introduce a theory of relative open Gromov-Witten invariants defined in a joint work with J. Solomon. 
This theory counts J-holomorphic disks with Lagrangian boundary in a symplectic manifold endowed with a compatible 
real structure subject to tangency condition with a smooth real divisor. I will emphasize the difficulties we have to face 
in our new theory compared to the absolute case  presented in the first talk.



 

Tuesday,  September 21 2010

Speaker:  Rares Rasdeaconu, Vanderbilt University

Title: Relative Open Gromov-Witten Invariants III

Abstract: In the last talk of the series we will present some relevant examples leading to a solution to the combinatorial 
problem left open in the second talk.



 

 

Sat. Sun. 25, 26 September 2010 Workshop in Kahler and Differential Geometry

Tuesday,  September 28 2010 This week's seminar is rescheduled on Tu. Oct 5

Speaker: Mehdi Lejmi, Vanderbilt University

Title: Extremal Metrics I 

Abstract: 

Tuesday, October 5 2010

Speaker: Mehdi Lejmi, Vanderbilt University

Title: Extremal Metrics I

Abstract: In this talk, we study first holomorphic vector fields on any compact Kahler 
manifold. Then, we introduce the notion of extremal Kahler metrics in the Calabi sense 
and we compute the first derivative of the Calabi functional to show that for an extremal
Calabi Kahler metric the scalar curvature is a Killing potential. Then, we state the 
Calabi theorem which gives an orthogonal decomposition of the Lie algebra of holomorphic 
vector fields. This provides a criterion for non-existence of extremal Calabi Kahler metrics.

Tuesday, October 12 2010

Speaker: Mehdi Lejmi, Vanderbilt University

Title: Extremal Metrics II

Abstract: In this talk, we sketch the proof of Calabi theorem which states that for any 
compact extremal Kahler manifold the isometry group is maximal in the group of automorphisms 
of the complex structure. In the special case of compact Kahler-Einstein manifold, we present a 
theorem due to Matsushima which gives a decomposition of the Lie algebra of holomorphic vector 
fields and a lower bound for positive eigenvalues of the Riemannian Laplacian acting on functions.

Tuesday, October 19 2010

Speaker: Mehdi Lejmi, Vanderbilt University

                  Title: Extremal Metrics III
    
                  Abstract: In this talk, we define the notion of the Futaki invariant. The non-vanishing of the the Futaki
                    invariant is an obstruction to the existence of Kahler metrics of constant scalar curvature in the set of
                    Kahler metrics whose the Kahler form belongs to a fixed Kahler class. As observed by Donaldson, the
                    Futaki invariant appears also in an algebraic expression which still make sense for a large class of singular
                    varieties.

Tuesday, October 26 2010

Speaker: Mehdi Lejmi, Vanderbilt University

                  Title: Extremal Metrics IV
    
                  Abstract: In this talk, we discuss the existence and the uniqueness of extremal Kahler metrics. The conjectures
                     about the existence and the uniqueness are derived from the geometric invariant theory in the finite dimensonal
                     case. So, we will present some elements of the geometric invariant theory and summarize the existence results.

Wednesday, November 3, in the Topology & Group Theory Seminar

Speaker: Ioana Suvaina, Vanderbilt University

                  Title: ALE Ricci Flat Kahler 4-Manifolds
    
                  Abstract:

Tuesday, November 9, 2010

Speaker: Basak Gurel, Vanderbilt University

                  Title: Action and Index Spectra and Periodic Orbits of Hamiltonian Systems I     

                  Abstract:

Tuesday, November 16, 2010

Speaker: Basak Gurel, Vanderbilt University

                  Title: Action and Index Spectra and Periodic Orbits of Hamiltonian Systems  II     

                  Abstract:

 

Old Seminar Web-Pages: Fall 2009