IWoAT Summer School 2026 | Stable Homotopy Theory

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.

Syllabus and Schedule

Syllabus (PDF)

Location: Lecture hall, Siyuan building, AMSS, Chinese Academy of Sciences, Beijing.

Monday, August 10, 2026

9:15-9:30 Opening remarks
9:30-10:30 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

9:30-10:30 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

9:30-10:30 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

9:30-10:30 Units and Thom spectra
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

9:30-10:30 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

Andrew J. Blumberg, Columbia University

Aowen Fan, Chinese Academy of Sciences

Courtney Hauf, University of Colorado Boulder

Yueshi Hou, University of California San Diego

Yifan Jin, Beijing Normal University

Runji Li, University of California Los Angeles

Xiansheng Li, Southern University of Science and Technology

Yuxuan Li, Tsinghua University

Sihao Ma, University of California Los Angeles

Stephanie Oh, University of Colorado Boulder

Alex Waugh, University of Washington/New Mexico State University

Yuchen Wu, University of California San Diego

Shangjie Zhang, University of California, San Diego / University of Washington

Shuhan Zheng, Fudan University

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.

Organizers

Committee Chair

Andrew J. Blumberg, Columbia University

Organizers

Hana Jia Kong, Zhejiang University

Guchuan Li, Peking University

Weinan Lin, Fudan University

Yunze Lu, Zhejiang University

Guozhen Wang, Fudan University

Zhouli Xu, University of California, Los Angeles

Zhengyi Zhou, Chinese Academy of Sciences

Yifei Zhu, Southern University of Science and Technology

Foling Zou, Chinese Academy of Sciences