MATH6032 - Topics in Algebra II - 2020/21

General Information

Lecturer

• Xuhua He
  • Office: LSB201
  • Email:

Course Description

In the tropical algebra, the sum of two numbers is their minimum, and the product is their sum. This makes polynomials into piecewise-linear functions and their zero sets into polyhedral complexes. Tropical geometry is a young subject that has undergone rapid development since the beginning of the 21st century. It provides a combinatorial shadow of algebraic geometry and algebraic groups, and reveals new and sometimes unexpected connections among different mathematical branches.

In this course, I will provide an introduction to tropical geometry, with some applications to Lusztig's theory of total positivity. Some knowledge of basic algebraic geometry will be helpful, but not strictly necessary.

References

• Diane Maclagan and Bernd Sturmfels, Introduction to Tropical Geometry, Graduate Studies in Mathematics 161, 2015.

Lecture Notes

• Week 1
• Week 2
• Week 3
• Week 4
• Week 5
• Week 6
• Week 7
• Week 8
• Week 9
• Week 10
• Week 11
• Week 12
• Week 13
• Week 14

Assignments

• Homework 1 (Due Feb 24)
• Homework 2 (Due March 31)

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

and thereby help avoid any practice that would not be acceptable.