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\title{Titles and Abstracts}
\author{http://math.nju.edu.cn/conference/2011/ }
\date{2011.7.26-29}
\maketitle


{\bf Jingyi Chen}  (University of British Columbia)

{\bf Title}: Recent progress on mean curvature flow for entire Lagrangian graphs


{\bf Gui-Hua Gong}  (University of Puerto Rico, USA)

{\bf Title}: Non-commutative Geometry, Positive Scalar Curvature, and the Strong Novikov Conjecture.

{\bf Abstract}: In this talk, I will explain how to use non-commutative geometry to study positive
scalar curvature problem of Gromov and Novikov conjecture.


{\bf Bo Guan}  (Ohio State University)

{\bf Title}: Hypersurfaces of constant curvature in Euclidean and hyperbolic spaces


{\bf Jiaxing Hong}  (Fudan University)

{\bf Title}: Estimates Near Boundary for Degenerate Elliptic Monge-Ampere Equations


{\bf Yi-Zhi Huang}  (Rutgers University, USA)

{\bf Title}: Riemannian Manifolds and representations of vertex operator algebras

{\bf Abstract}: Conjectures by physicists on nonlinear sigma-models are one of the most
influential source of inspirations and motivations for many recent works in geometry.
Unfortunately nonlinear sigma-models are still not mathematically constructed. I will
review some of the attempts to construct such theories and discuss why they do not give
the correct theories. I will also propose a program to give such a construction based on
my recent work on representations of vertex operator algebras that are not necessarily
semisimple.

{\bf Jiayu Li}  (University of Science and Technology of China)

{\bf Title}: Pinching conditions on symplectic mean curvature flows

{\bf Xiaobo Liu} (University of Notre Dame, USA)

{\bf Title}: The genus-1 Virasoro conjecture for Gromov-Witten Invariants.

{\bf Abstract}: The Virasoro conjecture predicts that the generating function for Gromov-Witten
invariants of smooth projective varieties is annihilated by a sequence of differential
operators which form a half branch of the Virasoro algebra. This conjecture was proposed
by physicists Eguchi, Hori, and Xiong and modified by S. Katz. In case that the target
manifold is a point, this conjecture is equivalent to Witten's conjecture, proved by
Kontsevich, that the generating fucntion of intersection numbers on the moduli spaces of
stable curves is a tau function of the KdV hierarchy. The genus-0 Virasoro conjecture was
proved by Tian and myself. Dubrovin and Y. Zhang proved the genus-1 part of this conjecture
for manifolds with semisimple quantum cohomology. In this talk, I will explain the current
state for the genus-1 Virasoro conjecture for manifolds whose quantum cohomology may not
be semisimple.


{\bf Peng Lu} (University of Oregon, USA)

{\bf Title}: Some geometric properties of gradient Ricci solitons

{\bf Abstract}: We discuss first a necessary and sufficient condition for Ricci shrinkers to have
posive asymptotic volume ratio, then the lower bounds for the scalar curvatures of noncompact
gradient Ricci solitons and a weak Ricci curvature bounds for the solitons, finally the
linearized Ricci flow.

{\bf Jie Qing} (UCSC, USA)

{\bf Title}: Ricci flow and conformally compact Einstein metrics


{\bf Xiaochun Rong}  (Capital Normal Univeristy and Rutgers University)

{\bf Title}: Injectivity radius estimate of pinched positively curved metrics

{\bf Abstract}: Let $M$ be a closed manifold. We prove that if
$M$ admits a metric $g$ with sectional curvature $0<\delta\le
\text{sec}_g\le 1$, then the injectivity radius of $g$ is
bounded below by $i(M,\delta)>0$, a constant depending only
on $M$ and $\delta$. This solves a conjecture of Klinginberg-Sakai.


{\bf Victor Schroeder}  (University of Zurich, CH)

{\bf Title}: Rigidity of Moebius structures


{\bf Lorenz Schwachhoefer} (University Dortmund, Germany)

{\bf Title}: Hyperbolic monopoles and pluricomplex geometry

{\bf Abstract}: We investigate the moduli space of hyperbolic monopoles which are
instatons with a certain symmetry group. We show that this moduli space
has a very special geometric structure: it admits a family of complex
structures, parametrized by the 2-sphere, but it is not hypercomplex. This
structure sheds some light on the geometry of this space.


{\bf Takashi Shioya} (Tohoku University, Japan)

{\bf Title}: Measure concentration and eigenvalues of Laplacian

{\bf Abstract}: Gromov developped a geometric theory of measure concentration, which is useful to
study the asymptotic behavior of a sequence of Riemannian manifolds with dimensions going to
infinity. Although Gromov omitted the details of proofs, we veryfy some parts of his proofs.
Using it, we study the asymptotic behavior of the eigenvalues of the Laplacian if the
Riemannian manifolds have nonnegative Ricci curvature.

This is a joint work with Kei Funano (RIMS).

{\bf Gang Tian} (Princeton University)

{\bf Title}: Symplectic curvature flow


{\bf Hongyu Wang}  (Yangzhou University)

{\bf Title}: J-anti invariant cohomology

{\bf Yusheng Wang}  (Beijing Normal University)

{\bf Title}:  On the Cayley-Klein-Hilbert metric;

{\bf Abstract}: In this talk, we will give a `new' and uniform viewpoint on the Cayley-Klein-Hilbert
metric in classical Riemannian geometry. And we will give some applications.

{\bf Shicheng Xu}  (Nanjing University)

{\bf Title:}: Fibrations from Alexandrov spaces to manifolds and their stability

{\bf Abstract}: It follows from Perelman's fibration theorem that a map preserving
metric balls from an Alexandrov space to a Riemannian manifold is a
locally trivial fibration. By Perelman's stability theorem, such maps
are stable under Gromov-Hausdoff convergence if no collapsing occurs.
We will talk about these properties for maps which are almost
preserving metric balls.


%{\bf Xiaoping Yang}  (Nanjing University of Science and Technology)
%
%{\bf Title}: On sub-Riemannian geodesics in CC spaces


{\bf Weiping Zhang}  (Nankai University)

{\bf Title}: Geometric quantization on noncompact manifolds

{\bf Abstract}: We present a joint work with Xiaonna Ma on the geometric quantization on noncompact
manifolds. It is a generalization of the Guillemin-Sternberg conjecture to the case of a compact
Lie group acting on a noncompact symplectic manifold. It also resolves a conjecture of Vergne.


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