Program
Generalized Teichmüller Spaces, Spin Structures and Ptolemy Transformations
Student No.:80
Time:Fri 16:30-17:30, Nov.23
Instructor:葉智皓 Ivan Ip  
Place:Lecture hall, Jin Chun Yuan West Bldg.
Starting Date:2018-11-23
Ending Date:2018-11-23

Abstract:
Teichmüller space is a fundamental space that is important in many areas of mathematics and physics. In recent times generalizations of this space have been intensely studied. Examples of such higher Teichmüller spaces are given by the so-called super-Teichmüller spaces, with structural groups given by supergroups. These appear as a natural object when studying a combinatorial approach to spin structures on Riemann surfaces and the generalization to supermanifolds. In this talk, we give a substantial simplification of the formulation of the spin structures and describe the N=1 and N=2 super-Teichmüller space using the analogue of Penner coordinates. (Joint work with Robert Penner and Anton Zeitlin.)


About speaker:
Ivan Ip joined Hong Kong University of Science and Technology (HKUST) as an Assistant Professor since June 2018. Prior to his appointment in HKUST, he stayed in Japan for 6 years as an Assistant Professor at Kyoto University from 2015-2018, and a Project Researcher at Kavli IPMU, Tokyo University from 2012-2015. He grew up in Hong Kong and was an IMO Medalist for the Hong Kong team in 2002. He received his B.Sc. in Mathematics and Physics from HKUST, and his Ph.D. in Mathematics from Yale University under the supervision of Igor Frenkel.



摘要:
泰西米勒空间是数学和物理领域中非常重要的一个基本空间,近年来对该领域的研究十分热门。超泰西米勒空间是这种高等泰西米勒空间的例子,其结构群由超群给出。当研究黎曼曲面上自旋结构的组合方法及其对超流形的推广时,这些作为自然物体呈现。
在本次报告中,主讲人将对自旋结构的公式进行实质性的简化,并使用Penner坐标的类似物来描述N=1和N=2超泰西米勒空间。(与Robert Penner和Anton Zeitlin合作。)


报告人简介:
葉智皓,香港科技大学助理教授。2012年-2015年在日本东京大学宇宙物理与数学研究所担任项目研究员,2015年-2018年在日本京都大学担任助理教授。他成长于香港,是2002年国际数学奥林匹克竞赛(IMO)奖牌得主,毕业于香港科技大学获数学与物理学士学位,并在美国耶鲁大学获得博士学位,导师为Igor Frenkel。