### 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)

- 10:00–10:30,
**Jiacheng Liang**,*Master's thesis defense: Elliptic cohomology theories and the $\sigma$-orientation* - 10:50–11:20,
**Zhonglin Wu**,*Master's thesis defense: Spectral sequence calculation for unstable $v_n$-periodic homotopy groups of spheres* - 3:00–3:45,
**Xuecai Ma**,*Doctoral thesis defense: Methods of spectral algebraic geometry in chromatic homotopy theory* - 4:30–5:00,
**Yunhao Sun**,*Master's thesis proposal: Algebraic cobordism and cycle class map*

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)

- 15:00–16:00,
**Yifan Wu**,*Transchromatic generalized character* - 16:30–17:30,
**Jiacheng Liang**,*$\infty$-topos and parametrized homotopy theory*

Jun 18, '24 (Tuesday in M5024)

- 9:30–10:30,
**Tongtong Liang**(University of California San Diego),*Geometric invariants in Adams spectral sequences* - 11:00–12:00,
**Xuecai Ma**,*Analytic Geometry and Homotopy Groups of the $K(n)$-Local Sphere* - 14:30–15:30,
**Yunhao Sun**,*Kerz-Strunk-Tamme's vanishing theorem on $K$-theory* - 16:00–17:30,
**Langwen Hui**(University of Illinois Urbana-Champaign),*Algebraic $K$-theory of finite fields*

### 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*