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 Spring 2024 (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,
On the existence of Adams's classical $v_1$-periodicity and 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 7, '24,
Wenhui Yang,
TBA
May 14, '24,
Peng Huang,
TBA
May 21, '24,
Zhou Fang,
TBA
May 28, '24,
Chenlu Huang,
TBA
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
June 7, '21, Huiyuan 3-518,
Tongtong Liang,
Steenrod operations