数学与统计学院 数学中心学术报告
A counting formula for Chern character numbers
冯惠涛 (重庆理工大学数学与统计学院)
An Introduction to Gromov-Witten Theory
傅勇 (重庆理工大学数学与统计学院)
时间：2011年12月23日（星期五）14:00~~16:00
地点：数学与统计学院422会议室
报告简介：
（1）14:00~~15:00
题目： A counting formula for Chern character numbers
冯惠涛 (重庆理工大学数学与统计学院)
In this talk， we will give a counting formula for Chern character numbers of complex super vector bundles. As an application, a Poincare-Hopf-type formula for complex-valued vector fields will be established.
（2）15:00~~16:00
题目： An Introduction to Gromov-Witten Theory
傅勇 (重庆理工大学数学与统计学院)
Gromov-Witten theory is a very active subject in algebraic geometry both for its applications in mathematics and its relations to physics. In this talk ，I will make a general introduction to some aspects around the theory.
报告人简介：
冯惠涛, 重庆理工大学数学与统计学院 教授, 南开大学陈省身数学所兼职教授、兼职博导，
1997博士毕业于中科院数学所。从事专业为微分几何， Atiyha—Singer 指标理论及其应用。
傅勇，重庆理工大学，PhD, University of Illinois
(1)、
Chern classes are characteristic classes. They are topological invariants associated to vector bundles on a smooth manifold. The question of whether two ostensibly different vector bundles are the same can be quite hard to answer. The Chern classes provide a simple test: if the Chern classes of a pair of vector bundles do not agree, then the vector bundles are different. The converse, however, is not true.
In topology, differential geometry, and algebraic geometry, it is often important to count how many linearly independent sections a vector bundle has. The Chern classes offer some information about this through, for instance, the Riemann-Roch theorem and the Atiyah-Singer index theorem.
Chern classes are also feasible to calculate in practice. In differential geometry (and some types of algebraic geometry), the Chern classes can be expressed as polynomials in the coefficients of the curvature form。
(2)、
In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish symplectic manifolds that were previously indistinguishable. They also play a crucial role in closed type IIA string theory. They are named for Mikhail Gromov and Edward Witten。
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