## Higher structures and index theory

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

#### Organizers

Fei Han(National University of Singapore)

Yunhe Sheng (Jilin University)

Yong Wang(Northeast Normal University)

Chenchang Zhu (Goettingen University)

#### Speakers

[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]

非交换环面上的正上圈

我们将遵循Connes的想法，讨论二维非交换环面上的正上圈的一些相关性质

### Schedule (TBA)

| | | |
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| Time | Speaker | Title |

Sep 28 | 9:00-10:00 | Wang Hang | An introduction to index theory of invariant Dirac operators |

| 10:30-11:30 | Wang Hang | An introduction to index theory of invariant Dirac operators |

| 15:00-16:00 | Bailing Wang | Natural higher structures in geometry and topology |

| 16:30-17:30 | Bailing Wang | Gerbes, D-branes and index theory |

Sep 29 | 9:00-10:00 | Hu Jianxun | Uniruled symplectic orbifold |

| 10:30-11:30 | Hu Jianxun | Uniruled symplectic orbifold |

| 15:00-16:00 | Yao Yijun | 非交换环面上的正上圈 |

| 16:30-17:30 | Yao Yijun | 非交换环面上的正上圈 |