About
IWoAT Summer School 2026: Stable homotopy theory will take place at the Academy of Mathematics and Systems Science (AMSS) of Chinese Academy of Sciences in Beijing, China from Monday, August 10 to Friday, August 14, 2026. The main topic of the summer school is stable homotopy theory, the modern theoretical foundation of algebraic topology. The Scientific Committee is chaired by Prof. Andrew J. Blumberg (Columbia University). The summer school is aimed at advanced undergraduates, graduate students, postdoctoral fellows, and researchers interested in algebraic topology and stable homotopy theory.
Award
We are pleased to announce the recipients of the IWoAT Summer School 2026 Outstanding Student Award: Gold Award: Chuyun Yang 杨楚云 (Peking University), Aowen Fan 范骜文 (Chinese Academy of Sciences) Silver Award: Shangcheng Hao 郝尚诚 (Shanghai Jiao Tong University), Yong Liu 刘泳 (AMSS, Chinese Academy of Sciences), Shimin Zhao 赵世民 (Zhejiang University) Bronze Award: Xinyu Liu 刘新宇 (Capital Normal University), Lirui Pang 庞力睿 (University of Toronto), Pengxiang Wang 王鹏翔 (Capital Normal University), Xingzhi Huang (University of Wisconsin–Madison), Zheng Ma 马铮 (University of Science and Technology of China) Congratulations to all awardees, and thank you to every participant for your hard work.Syllabus and Schedule
Syllabus (PDF)
Location: Lecture hall, Siyuan building, AMSS, Chinese Academy of Sciences, Beijing.
Monday, August 10, 2026
09:15-09:30 Opening remarks 09:30-10:30 Overview 11:00-12:00 Model categories 14:00-15:00 Simplicial (model) categories 15:30-16:30 (∞,1)-categories 19:00-20:00 Problem session
Tuesday, August 11, 2026
09:30-10:30 Diagram spectra; symmetric, orthogonal, excisive functors 11:00-12:00 Γ-spaces 14:00-15:00 Stable model categories, SM7 revisited 15:30-16:30 Spectra and excisive functors in (∞,1)-categories
Wednesday, August 12, 2026
09:30-10:30 The model structures on rings and modules in diagram spectra 11:00-12:00 Morita theory, module categories, bar constructions and cyclic bar constructions 14:00-15:00 Operads 15:30-16:30 Eilenberg-Mac Lane spectra, HM-modules, and chain complexes 19:00-20:00 Problem session
Thursday, August 13, 2026
09:30-10:30 Units and Thom spectra [Slides] [PSet] 11:00-12:00 THH and TAQ; construction, definition, basic properties 14:00-15:00 Algebraic K-theory; inputs as Waldhausen categories, stable categories 15:30-16:30 Picard and Brauer groups, generalized Thom spectra
Friday, August 14, 2026
09:30-10:30 Localization and local objects 11:00-12:00 Localization in the stable setting, stable ∞-categories and localization, symmetric monoidal structures 13:20-14:20 A brief introduction to chromatic localizations and the chromatic perspective on the stable category 14:30-15:30 Visions of spectral algebraic geometry 16:00-17:00 Special Event: Morningside high-level academic lecture series by Prof. Zhouli Xu
Lecturers
Application
Everyone interested is welcome to attend. Due to limited space, we kindly ask you to register in advance. Limited funding support may be available for eligible participants.
To register, please complete the online registration form by June 27, 2026.