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**

**Monday****,
October 8th, **

__Speaker:__** ****Marcelo Disconzi, ****Vanderbilt
University****
**

__Title__**: ****Compactness
results
for
the
Yamabe
problem,
III**

**Monday****,
October 15th, **

__Speaker:__** ****Caner Koca, ****Vanderbilt
University****
**

__Title__**: ****Positively
Curved
Einstein
Manifolds
in Dimension Four, I**

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)**

**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 (rescheduled)**

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