# Differential Geometry Seminar Schedule for
Spring 2003

# Fridays 3:30 - 4:30pm, SH 6617

### 4/4 Xianzhe Dai, UCSB
``A Positive Mass Theorem for Spaces compactified on a Calabi-Yau"

### 4/11 Guofang Wei, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 7.3"

### 4/18 Vitali Kapovitch, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 8"

### 4/25 Vitali Kapovitch, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 8,9"

### 5/2 Vitali Kapovitch, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 8,9"

### 5/9 Vitali Kapovitch, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 9"

### 5/16 Rugang Ye, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 11.2 and Lemma 1.2 in
the second paper"

### 5/23 Rugang Ye, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 11"

### 5/30 Rugang Ye, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 11"

### 6/6 Fred Wilhelm, UCR
`` A Preliminary Report on Counter Examples to the Uniform
Pinching Conjecture"

# Differential Geometry Seminar Schedule for
Winter 2003

# Fridays 3:30 - 4:30pm, SH 6617

### This quarter's geometry seminar we will focus on
``Ricci flow and geometrization of 3-manifolds".

Thurston's geometrization program for 3-manifolds
seeks to
classify 3-manifolds based on homogenous geometries. Hamiltonhas developed the
approach of Ricci flow to achieve geometrization. Recently, Perelman wrote an
very important paper on this subject. We will go through this paper.
The paper is at arXiv: math.DG/0211159
and can be down load at
http://front.math.ucdavis.edu/search?a=Perelman%2C+G*&t=&q=&c=&n=40&s=Abstracts
### 1/10 organization meeting

### 1/17 Rugang Ye, UCSB
``Ricci flow and geometrization of 3-manifolds, introduction"

### 1/24 Rugang Ye, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 1"

### 1/31 Guofang Wei, UCSB
``Ricci flow and geometrization of 3-manifolds, Sections 3,4"

### 2/7 see interview talk

### 2/14 Guofang Wei, UCSB
``Ricci flow and geometrization of 3-manifolds, Section 7"

### 2/21 no meeting

### 2/28 Vitali Kapovitch, UCSB
``Non-singular solutions of Ricci flow on 3-manifolds, by R. Hamilton"

### 3/7 Vitali Kapovitch, UCSB
``Non-singular solutions of Ricci flow on 3-manifolds, by R. Hamilton"

### 3/14 Vitali Kapovitch, UCSB
``Non-singular solutions of Ricci flow on 3-manifolds, by R. Hamilton"

### 3/19 (special day) Xiaowei Wang, UCLA
``Canonical metrics on vector bundles over a projective manifold"

Abstract:
The interplay between algebraic geometry and differential geometry has
long history start from Hodge, Kodaira, Yau, Tian and more recently
Donaldson. The existence of special metric on a vector bundle or a
manifold helps us to get many insights into their algebro-geometric
property and vice versa. In this talk, I will discuss a metric
characterization of whether a vector bundle over a projective manifold
being stable or not in GIT sense, and it's relation with the classical
Donaldson-Uhlenbeck-Yau picture.
# Differential Geometry Seminar Schedule for
Fall 2002

# Fridays 3:30 - 4:30pm, SH 6617

### 9/27 no meeting

### 10/4 Xiangyu Zhou, Chinese Academy of Science
``Extended future tube conjecture"

Abstract: The
extended future tube conjecture originated from Quantum field theory at
the end of 1950's. In the present talk, we'll explain what the conjecture
is and outline the main idea of our solution of the conjecture.
### 10/11 Vitali Kapovitch, UCSB
``Biquotients with singly generated rational cohomology"

Abstract:
We classify all biquotients whose rational cohomology rings are
generated by one element. As a consequence we show that the
Gromoll-Meyer $7$-sphere is the only exotic sphere which can be
written as a biquotient.
### 10/18 Rugang Ye, UCSB
``A new mathematic model of the Plateau problem for minimal surfaces"

Abstract: The classical Plateau problem models the experiment of
spanning soap films in a wire frame. New measurements yield that soap
films are extremely thin (a few nm!), and hence the wire frame should not
be treated as a curve. Rather, it should be treated as a torus like surface.
We present a new treatment of the problem.
### 10/25 Yue Lei, UCSB
``An index theorem on open manifolds of John Roe"

Abstract: We discuss a series of two papers by John Roe. In the first
he proves an abstract index theorem for Dirac type operators
on noncompact manifolds with bounded geometry. In the second
he gives some concrete applications of this result. The papers
are published in J. Diff. Geom. 27 (1988).

### 11/1 Yue Lei, UCSB
``An index theorem on open manifolds of John Roe, continued"

### 11/8 Rugang Ye, UCSB
``Some recent results on the Yamabe invariant of 3-manifolds"

### 11/15 John Ennis, UCSB
``A finiteness theorem for Ricci curvature in dimension three of S. Zhu"

### 11/22 no meeting, see colloquium

### 11/29 Thanksgiving

### 12/6 Xianzhe Dai, UCSB
``Eta invariants for manifolds with boundary"

Abstract: The eta invariant for a closed manifold is introduced by
Atiyah-Patodi-Singer
as the boundary correction term in the index formula for manifold with
boundary. It has found many significant
applications in various fields such as number theory, mathematical physics,
Jones-Witten theory, Floer homology, gauge theory
and low dimensional topology . There are now various work
generalizing it to manifolds with boundary. We discuss the natural and
interesting question of the relationships among the various generalizations.
It turns out that they all coincide.
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