Objectives: A pre-school series of lectures on selected topics in Galois cohomology, modular forms, and class field theory will be organized to prepare the participants for the main topics of the summer school.

Time: May 2024, Location: VIASM

Learning mode: Hybrid (Offline at VIASM and Online via Zoom)

Registration: If you wish to attend the pre-school, please register here. Registration is mandatory and applies to both the pre-school and the summer school on Galois representations and Reciprocity.

Topics:

• Course 1: Algebraic number theory (5 lectures): Ring of integers, unique factorization of ideals, class group, decomposition, inertia group and Frobenius, Chebotarev density theorem, local and global fields, adeles.
  Suggested reference: Chapter 1 of “Algebraic Number Theory: Proceedings of an     Instructional   Conference Organized by the London Mathematical Society”, J.W.S.Cassels (editor) and A.Frohlich (editor).
• Course 2: Class field theory (2 lectures): statement of local and global class field theory, maybe examples if there is time.
  Suggested reference:  “Algebraic Number Theory: Proceedings of an Instructional   Conference organized by the London Mathematical Society”, J.W.S.Cassels (editor), A.Frohlich (editor), or “Class Field Theory”, E.Artin and J.Tate.
• Course 3: Galois cohomology and Tate duality (3 lectures): cohomology of (pro-)finite groups and basic properties, local and global Tate duality, Poitou-Tate.
  Suggested reference: “Cohomology of Number Fields, J.Neukirch, A.Schmidt and K. Wingberg.
• Course 4: An introduction to modular forms (4 lectures): modular curves, Hecke operators.
  Suggested reference: “A First Course in Modular Forms”, F.Diamond and J.Shurman.

Lecturers:

• Course 1 - Algebraic number theory: Dr. Nguyen Xuan Tho (Hanoi University of Science and Technology, Vietnam) 
• Course 2 - Class field theory: Mr. Pham Ngo Thanh Dat (Universite Paris 13, France)
• Course 3 - Galois cohomology: Assoc. Prof. Nguyen Duy Tan (Hanoi University of Science and Technology, Vietnam) 
• Course 4 - Modular forms: Dr. Ngo Trung Hieu (Institute of Mathematics, VAST, Vietnam)

Pre-school Program:

Tuesday mornings and Sunday mornings. The time indicated here is Hanoi timezone (GMT +7).

• First lecture: 8:00-9:20
• Second lecture: 9:40-11:00

* The lectures on Sunday 26/5 are in the afternoon from 1pm to 4pm.