A survey of group actions and applications in mathematical sciences | |
Student No.： | 50 |
Time： | Part 1: June 19, July 3,5,8；Part 2: 2013-07-22 ~ 2013-08-21 |
Instructor： | Lizhen Ji [University of Michigan] |
Place： | Conference Room 1, Floor 1, Jin Chun Yuan West Building |
Starting Date： | 2013-6-17 |
Ending Date： | 2013-8-25 |
【Schedule updated】Lecture on July 1 will be changed to July 5 at Conference Room 3, Floor 3, Jin Chun Yuan West Building
Title:
Part 1:A survey of group actions and applications in mathematical sciences
Part 2: Introduction to tropical geometry and applications
Schedule:
Part 1: June 19, July 3,5,8
Time: Mon/Wed 13:00-14:50
Place: July 3/8/19 Conference Room 1; July 5 Conference Room 3
Part 2: 2013-07-22 ~ 2013-08-21
Time: Mon/Wed 13:00-14:50
Place: Conference Room 1
Description:
Part 1: Since groups were introduced and used by Galois, they have becoming an essential part of modern mathematics. According to a letter Lie wrote to Klein in October 1882: ``Poincare mentioned on one occasion that all of mathematics is a matter of groups." The power, usefulness and beauty of groups come from their actions. In this series of lectures, I will give a survey of how group actions arise and how they can be used to study many problems to explain the meaning of the assertion of Poincare.
Part 2: Tropical geometry is a new and hot subject in mathematics. It has been used to study many problems in algebraic geometry, geometrical group theory, and topology etc. Tropical varieties are piece-wise linear objects with integral affine structures. For some applications, they simplify and catch the essential properties of algebraic varieties. Since tropical geometry is algebraic geometry over the tropical semifield which is quite different from the usual field of complex number, tropical varieties exhibit properties quite different from usual algebraic varieties. In these lectures, I will start from basics, give an introduction to tropical geometry, and then discuss some applications in algebraic geometry and geometric group theory.
Prerequisite:
Differential geometry and some group theory.