时间：2024年7月6日至7月7日

地点：安徽省合肥市中国科学技术大学东校区第五教学楼

学研会指定住宿酒店：安徽悦雅江南春酒店(金寨路店)

短课：

明爽，北京雁栖湖应用数学研究院

题目: On Witten's finiteness conjecture for skein modules

摘要：Witten conjectured the existence of a four-dimensional topological field theory(TFT) such that the vector space assigned to closed three-manifolds are the skein modules over C(q). A crucial step towards Witten's conjecture is to verify such skein modules are of finite dimensional over C(q)(Also called finiteness conjecture for skein modules). In this talk, we will discuss the proof of this finiteness conjecture by Gunningham, Jordan and Safronov with an emphasis on the fundamental ideas of the categorical approach in the study of quantum algebra and TFT. If time permit, we will also explore the analysis part of the proof.

田垠，北京师范大学

题目：Khovanov homology

摘要：This course is to give an introduction to categorification from topological and algebraic point of view. We will discuss Khovanov homology as a categorification of the Jones polynomial. On the algebraic side, we will discuss categorified quantum group theory, due to Khovanov-Lauda, Rouquier.

王骁，吉林大学

题目：Basics on skein modules and skein algebras

摘要：Skein modules are 3-manifold invariants. They were introduced independently by Przytycki and Turaev in the late 1980’s, and have since become one of important subjects to study in low dimensional topology. In this course, we will mainly focus on the Kauffman bracket skein module(KBSM) and the Kauffman bracket skein algebra(KBSA). Basic properties and examples will be provided. In particular, we will talk about how KBSM behaves under connected sum operation, the “product to sum formula” of  torus and the relation between KBSA and SL(2,C) characters.

朱盛茂，浙江师范大学

题目：Introduction to colored jones polynomial

摘要：In this short course, I first give the defintions of Jones polynomials and colored Jones polynomials via skein theory.  Then I will introduce a general method to compute the colored Jones polynomials, and present some structural properties for the colored Jones polynomials.

邹燕清，华东师范大学

题目：An introduction to Heegaard splitting

摘要：In 1898, Heegaard introduced a Heegaard splitting. After works of Moise, Bing and Haken, any compact orientable 3-manifold admits a Heegaard splitting.  This course will cover the following topics: Stabilization problem, Heegaard distance and Heegaard genus.

日程安排

7月6日

07：50-09：25 朱盛茂

09：45-11：20 朱盛茂

11：25-12：10 邹燕清

14：00-14：45 邹燕清

14：50-18：20 田垠

7月7日

07：50-09：25 邹燕清

09：45-11：20 王骁

11：25-12：10 王骁

14：00-14：45 王骁

14：50-18：20 明爽

会议组委会：刘毅，孙哲，杨志青