MATH6032 - Topics in Algebra II - 2021/22

General Information

Lecturer

• Xuhua He
  • Office: LSB201
  • Email:

Time and Venue

• Lecture: W9:30-12:15, LSB 222

Course Description

By definition, an invertible real matrix is called totally positive if all the minors are positive and called totally nonnegative if all the minors are nonnegative. These notions were introduced in the 1930s by Schoenberg. In 1994, Lusztig in his foundational work developed the theory of total positivity for arbitrary split real reductive group G. The theory of total positivity has significant impacts on many active research directions. In this course, we will give an introduction to the theory of total positivity. We will discuss the algebraic, combinatorial, and geometric properties related to the total positivity. We will also discuss some recent progress of the theory over semifields and discuss some open problems.

Lecture Notes

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