Target Audience: Undergraduate students, graduate students, postdocs, professors, not necessarily working in number theory.

Teaching Language: English

Mode of teaching: Online

Office hours: (updated on March 14)

There are face-to-face discussion sessions held fortnightly at Jingzhai 313 every Friday, 16:30 -17:30. These are“informal meetings in number theory, to help enjoy its areas, to answer questions, to discuss research literature and problems, to share stories.” All students of Tsinghua University, taking or not taking this course, are welcome to attend. (The next meeting is on March 24).

Notice(updated April 25th): Please be informed that the scheduled course sessions on Tuesday May 2, and Thursday May 4, have been canceled, and the course will resume on Tuesday, May 9.

Prerequisites:

Basic number theory and commutative algebra, such as congruences, quadratic reciprocity law, groups, commutative rings.

Description:

Researchers in one area are often unable to understand research work in another area, even inside number theory. Still, there are few common underlying fundamental theories that unite many areas. This first series of lectures will present some fundamental unifying theories in number theory. They will include class field theory and its three generalisations: higher class field theory, Langlands program, anabelian geometry. 

The course starts with topic 6 and continues to 7, 8, 9, etc.Discussion of topic 5 will be included in topic 8. Topic 9 will start approximately from lecture 13. 

Lecture notes of topics 1-5 are available:

First course in number theory

https://ivanfesenko.org/wp-content/uploads/Q/C1/Pr/firstnt.pdf

First course in commutative algebra

https://ivanfesenko.org/wp-content/uploads/Q/C1/Pr/firstca.pdf

Source:

This recent paper in the EMS Surveys: https://ivanfesenko.org/wp-content/uploads/2021/11/232.pdf 

Registration List Link：（Registration is encouraged to receive notices from the course.）

https://www.wjx.top/vm/hNd96OF.aspx#

Slides of the introductory lecture：

https://ivanfesenko.org/wp-content/uploads/Q/C1/L/l1.pdf

The lecture notes are available from

https://ivanfesenko.org/wp-content/uploads/Q/C1/partI.pdf 

The slides are available from

https://ivanfesenko.org/wp-content/uploads/Q/C1/L/antsl.pdf 

(algebraic number theory)

and

https://ivanfesenko.org/wp-content/uploads/Q/C1/L/cdvfsl.pdf 

(local fields and class field theory)

Videos:

http://archive.ymsc.tsinghua.edu.cn/pacm_course?html=Core_topics_in_modern_number_theory_I.html