2020 Advanced topics in Algebra F

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Suzuki Masatoshi 
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Intensive (Zoom)  
Group
-
Course number
MTH.A502
Credits
1
Academic year
2020
Offered quarter
4Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

The theory of automorphic L-functions is a major research area of modern number theory, and is nowadays becoming more and more important in several related areas of mathematics. This lecture aims to explain the basics of automorphic L-functions and to mention a recent breakthrough on the subconvexity problem. This lecture is based on Advanced topics in Algebra E.

Student learning outcomes

Students are expected to:
- obtain basic notions and methods related to automorphic L-functions,
- understand modern tools and concepts in the theory of automorphic L-functions,
- attain a deep understanding of the theory of automorphic L-functions.

Keywords

modular forms, automorphic representations, automorphic L-functions

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

This is a standard lecture course. There will be some homework assignments.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Automorphic representation of GL(n) Details will be provided during each class session
Class 2 Adelization of classical automorphic forms Details will be provided during each class session
Class 3 Eisenstein series Details will be provided during each class session
Class 4 Revisit the subconvexity problem Details will be provided during each class session
Class 5 The Burgess bound Details will be provided during each class session
Class 6 Integral representations of L-functions (1) Details will be provided during each class session
Class 7 Integral representations of L-functions (2) Details will be provided during each class session
Class 8 Subconvex bounds for Rankin-Selberg L-functions Details will be provided during each class session

Textbook(s)

None required.

Reference books, course materials, etc.

Details will be announced during the course.

Assessment criteria and methods

Course scores are evaluated by homework assignments (100%). Details will be announced during the course.

Related courses

  • MTH.A501 : Advanced topics in Algebra E
  • MTH.A301 : Algebra I
  • MTH.A302 : Algebra II
  • MTH.C301 : Complex Analysis I
  • MTH.C302 : Complex Analysis II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Basic undergraduate algebra and complex analysis

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