About

This is a graduate-level seminar on algebraic and geometric topology. Topics are selected from common interests of the participants. Here are some general suggestions on how to give a good talk.

Talks in Fall 2024 (mostly Mondays 4:20 in M5024)

Sep 23, '24, Yifan Wu, When is $K(n)^*(BG)$ concentrated in even degrees?

Sep 30, '24, Chunshuang Yin, An introduction to toric varieties

Oct 14, '24, Zeyang Ding, TBA

Talks in Spring 2024 (mostly Tuesdays 4:20 in M5024)

Mar 12, '24, Qingrui Qu, An introduction to singularity theory, Milnor's fibration theorem and Brieskorn's construction of exotic spheres

Mar 19, '24, Jiacheng Liang, Barr-Beck Theorem, Morita theory and Brauer groups in $\infty$-categories

Mar 26, '24, Yunsheng Li, The Teichmüller TQFT and the Quantum Modularity Conjecture

Apr 2, '24, Yunsheng Li, The Teichmüller TQFT and the Quantum Modularity Conjecture, II

Apr 9, '24, Yifan Wu, Pipe Rings and Pipe Formal Groups

Apr 16, '24, Qingrui Qu, From Adams's $v_1$-periodicity to Andrews's motivic $w_1$-periodicity in homotopy groups

Apr 23, '24, Jiacheng Liang, Picard $\infty$-groupoids, Picard groups of $\mathbb{E}_\infty$–rings and generalized Thom spectra

Apr 30, '24, Yunhao Sun, Motives, motivic cohomology, and motivic homotopy: A historical introduction

May 14, '24, Peng Huang, Functoriality of the Postnikov tower

May 15, '24 (Wednesday in M4009)

May 21, '24, Zhou Fang, Wenhui Yang, Chenlu Huang, Topology and geometry of singularities

May 28, '24, Ni An, The colored Jones polynomial, Nahm sum and stability

Jun 4, '24, Zhonglin Wu, On "Secondary power operations and the Brown–Peterson spectrum at the prime 2"

Jun 14, '24, Zhonglin Wu, On "Secondary power operations and the Brown–Peterson spectrum at the prime 2", II

Jun 17, '24 (Monday in M616)

Jun 18, '24 (Tuesday in M5024)

Talks in Fall 2023 (Tuesdays 4:20 in M4009)

Oct 17, '23, Yifan Wu, Dyer–Lashof theories and algebras

Nov 7, '23, Zhonglin Wu, The motivic Adams spectral sequence

Nov 28, '23, Qingrui Qu, On "The special fiber of the motivic deformation of the stable homotopy category is algebraic"

Dec 5, '23 (4:20, Yidan 307), Yunhao Sun, On "The Chow $t$-structure on the $\infty$-category of motivic spectra"

Dec 6, '23 (4:20–5:10, M5024), Wenbo Liao (Chinese University of Hong Kong), Guts of sutured manifolds and knots

Dec 19, '23 (4:20, M1001), Qingrui Qu, Chromatic structures in motivic and equivariant stable homotopy categories

Dec 26, '23, Jiacheng Liang, An overview of $\infty$-categories and higher algebra

Jan 4, '24 (4:20–5:10, M5024), Wenhui Yang, Homotopy theory for directed graphs

Talks in Spring 2023 (Tuesdays 4:20 in M5024)

Mar 7, '23, Yingxin Li, The Goerss–Hopkins obstruction theory

Apr 11, '23, Zhonglin Wu, Multiplicative structures in the Adams spectral sequence

Apr 18, '23, Xuecai Ma, Formal moduli problems

Apr 25, '23, Yuanding Li, An overview of $v_n$-periodic homotopy theory

May 9, '23, Yunhao Sun, An overview of motivic homotopy theory

May 16, '23, Hongxiang Zhao, Explicit local class field theory à la Lubin and Tate with an application to algebraic topology

May 17, '23 (10–11, M4009), Tongtong Liang, Thesis defense: Methods of homotopy theory in algebraic geometry from the viewpoint of cohomology operations

May 23, '23, Jiacheng Liang, Thom spectra, infinite loop spaces, generalized cocycles, and the $\sigma$-orientation

May 30, '23, Qingrui Qu, Functor calculus and chromatic homotopy theory

Talks in Fall 2022 (Tuesdays 4:20–5:20 / 4:20–6:10 in M5024)

Sep 20, '22, Jiacheng Liang, Elliptic Curves and Abelian Varieties

Sep 27, '22, Yifan Wu, Introduction to bordism and Thom spectra

Oct 11, '22, Tongtong Liang, Power Operations in Complex Cobordism and Quillen's Theorem on Formal Group Laws

Oct 18, '22, Zhonglin Wu, Introduction to Adams spectral sequence

Nov 15 & Nov 22, '22, Xuecai Ma, An overview of chromatic homotopy theory

Nov 29, '22, Hongxiang Zhao, Formal Group Laws and Formal Groups

Dec 6, '22, Jiacheng Liang, Sites, Sheaves, Formal Groups and Stacks

Dec 13, '22, Tongtong Liang, Operads and the Recognition Principle

Dec 20, '22, Tongtong Liang, An Introduction to Structured Ring Spectra

Jan 5, '23, Yingxin Li, Elliptic homology theory and tmf

Talks in Summer 2022

Jul 25, '22 (2:30–3:30, M2002), Xuecai Ma, Methods of spectral algebraic geometry in chromatic homotopy theory

Jul 25, '22 (3:30–4:30, M2002), Tongtong Liang, Methods of homotopy theory in algebraic geometry from the viewpoint of cohomology operations

Jul 28, '22 (4–5, M714), Kecheng Shi, Reciprocity and isogeny-based cryptography

Talks in Spring 2021 (mostly Mondays 4:30–5:30 in Yidan 307)

Apr 19, '21, Tongtong Liang, Homotopy coherence problem and ∞-categories

Apr 26, '21, Tongtong Liang, Introduction to spectral sequences

May 10, '21, Pengcheng Li, Introduction to spectral sequences, II

May 17, '21, Huiyuan 3-518, Siheng Yi, Rational homotopy theory

May 24, '21, Siheng Yi, Rational homotopy theory (cont'd)

May 31, '21, 10-11 am, Yifan Wu, K-theory

Jun 7, '21, Huiyuan 3-518, Tongtong Liang, Steenrod operations