## Higher structures and index theory ## *** Aug. 28-30, Changchun at [Department of Mathematics, Jilin University]( http://math.jlu.edu.cn/) *** ####Organizers#### [Fei Han](http://ww1.math.nus.edu.sg/onepageCV.aspx?id=mathanf)(National University of Singapore) [Yunhe Sheng](http://math.jlu.edu.cn/?mod=teacher&act=view&id=184) (Jilin University) [Yong Wang] ()(Northeast Normal University) [[Chenchang Zhu]] (Goettingen University) *** *** ####Speakers#### [Jianxun Hu] Uniruled symplectic orbifold [Bailing Wang](http://maths-people.anu.edu.au/~wangb/)(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)### | | | | | |-----|-----|----|-----| | | Time | Speaker|Title| |Aug 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| |Aug 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|