Print

2019　Advanced topics in Algebra H1

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Graduate major in Mathematics
Instructor(s)
Wakabayashi Yasuhiro 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Mon5-6(H102)  
Group
-
Course number
MTH.A508
Credits
1
Academic year
2019
Offered quarter
4Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

This course consists of mostly independent parts each of which includes a recent topic of the moduli space of (algebraic) curves.
Moduli theory is the study of the way in which algebraic varieties, or more generally, geometric objects attached to them, vary in families. The moduli space of curves has been studied since Riemann, but it was first rigorously constructed only in the 1960s by Mumford and others and the theory has continued to develop since then. In the last decades, the theory has experienced an extraordinary development, finding an increasing number of connections with many other areas of mathematics.
The aim of this course is to provide glimpses into some of the connections with arithmetic and algebraic geometry, such as tropical geometry, anabelian geometry, p-adic Teichmuller theory, etc.. (But, there is a possibility that course schedule may be modified.)

Student learning outcomes

By the end of this course, students will be able to:

(1) Obtain some knowledge of the recent development of the moduli space of curves.
(2) Understand the respective relationships between the moduli space of curves and certain notions in arithmetic and algebraic geometry.

Keywords

Moduli of (algebraic) curves, Tropical geometry, Anabelian geometry, Intersection theory, p-adic Teichmuller theory.

Competencies that will be developed

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

Class flow

Ordinary lectures. Assignments will be given during class sessions.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Moduli of curves and the basics (Introduction) Details will be provided during each class session.
Class 2 Moduli of curves and Tropical geometry
Class 3 Moduli of curves and Anabelian geometry I
Class 4 Moduli of curves and Anabelian geometry II
Class 5 Moduli of curves and Intersection theory I
Class 6 Moduli of curves and Intersection theory II
Class 7 Moduli of curves and p-adic Teichmuller theory I
Class 8 Moduli of curves and p-adic Teichmuller theory II

Textbook(s)

None in particular.

Reference books, course materials, etc.

Handouts will be distributed at the beginning of class when necessary.

Assessment criteria and methods

Assessments on reports.

Related courses

  • MTH.A201 ： Introduction to Algebra I
  • MTH.A202 ： Introduction to Algebra II
  • MTH.A301 ： Algebra I
  • MTH.A302 ： Algebra II
  • MTH.A507 ： Advanced topics in Algebra G1

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

Basic knowledge of scheme theory (e.g., R. Hartshorne, "Algebraic Geometry", GTM 52, Springer-Verlag, ISBN 0-387-90244-9).
Enrollment in the related courses is desirable.

Page Top