Higher Structure Conferences higherstructurechina V (Rev #5)

Higher structures and index theory

Aug. 28-30, Changchun at Department of Mathematics, Jilin University


Fei Han(National University of Singapore)

Yunhe Sheng (Jilin University)

Yong Wang(Northeast Normal University)

Chenchang Zhu (Goettingen University)


[Jianxun Hu]

Uniruled symplectic orbifold

Bailing Wang(Australian National University)

(1) Natural higher structures in geometry and topology

Abstract: In this talk, I will review some basics of topological spaces, smooth manifolds, and vector bundles and the role of cocycle conditions in their construction. Then I will explain how violations of the cocycle conditions lead to natural higher structures in geometry and topology:

orientation structures, spin structure and string structure. The talk will end with a 30-year outstanding question about Dirac operators on loop spaces.

(2) Gerbes, D-branes and index theory

Abstract: In this second talk, I will explain another notion of higher structures: gerbes, and its role in the study of D-branes. Then I will give a mathematical definition of D-branes and its relation to twisted version of Atiyah-Singer index theorem.

[Hang Wang]

An introduction to index theory of invariant Dirac operators

In the first hour I will introduce Dirac operators and some properties, on manifolds and manifolds with group actions, and definition of higher index. In the second hour I will talk about some variations of indices and their connections to representation theory.

[Yijun Yao]



Schedule (TBA)

Sep 289:00-10:00Wang HangAn introduction to index theory of invariant Dirac operators
10:30-11:30Wang HangAn introduction to index theory of invariant Dirac operators
15:00-16:00Bailing WangNatural higher structures in geometry and topology
16:30-17:30Bailing WangGerbes, D-branes and index theory
Sep 299:00-10:00Hu JianxunUniruled symplectic orbifold
10:30-11:30Hu JianxunUniruled symplectic orbifold
15:00-16:00Yao Yijun非交换环面上的正上圈
16:30-17:30Yao Yijun非交换环面上的正上圈

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