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​ZJU-Westlake Derived Algebraic Geometry Learning seminar II (Spring 2023)

2023-03-06 09:49:08
报告人 时间 13:00-15:00
地点 Zhejiang University 2023
月日 03-06

ZJU-Westlake Derived Algebraic Geometry Learning seminar II (Spring 2023)


Time and Location:

Monday 15:00-17:00 (every two weeks starting from March 06), Room 101, No. 2 Haina Building, Zijingang Campus, ZheJiang University.

Monday 15:00-17:00 (every two weeks starting from March 13), E4-201, Yungu Campus, Westlake University.

Organizer: Lifan Guan (Westlake) and Feng Wang (ZJU)

Contact: guanlifan@westlake.edu.cn, wfmath@zju.edu.cn


Tentative Plan:

In this semester, we continue to learn some basic derived algebraic geometry. This time, we will focus on higher category theory, which plays a central role in the more systematical approach (a la Lurie) to derived algebraic geometry. To begin, we will start by learning basic notations of infinity categories via the model of quasi-categories, following Lurie. Then we will move on to the basic theory of presentable infinity-categories, and infinity-topoi. If time permits, we will also discuss some stable infinity-categories. The main reference is Lurie’s HTT and HA [4, 5], as well as Cisinski [1] and Land [3].

More details can be found here.

Reference:

[1] D. Cisinski, Higher categories and homotopical algebra, Cambridge Studies in Advanced Mathematics, 180.

[2] M. Groth, A short course on 1-categories, avaiable online.

[3] M. Land, Introduction to infinity-categories, Compact Textbooks in Mathematics.

[4] J. Lurie, Higher topos theory, avaiable online.

[5] J. Lurie, Higher algebra, avaiable online.

[6] J. Lurie, Categorical logic, lecture notes avaiable online


Tentative Schedule (Rough plan)

Topic

Speaker

Time  and Location

An overview

Lifan Guan

13:00-15:00, March 6, ZJU

Simplicial model category, homotopy category and examples

Xing Gu

March 13, Westlake

Anodyne maps and fibrations

Yichang Cai

March 20, ZJU

Joining and slices, limits and colimits

TBD

March 27, Westlake

Cartesian and cocartesian fibrations, straightenings and unstraightenings

TBD

April 3, ZJU

Infinity categories of presheaves and localizations

TBD

April 10, Westlake

Presentable infinity categories I

TBD

April 17, ZJU

Presentable infinity categories II

TBD

April 24, Westlake

Infinity topoi I

TBD

May 8, ZJU

Infinity topoi II

TBD

May 15, Westlake

Infinity topoi III

TBD

May 22, ZJU

Stable infinity categories I

TBD

May 29, Westlake

Stable infinity categories II

TBD

June 5, ZJU