Course information
- Institution
- University of Waterloo
- Term
- Spring 2023
- Meeting time
- Tuesdays and Thursdays, 11:30am–12:50pm
- Room
- RCH 208
A graduate topics course on Lorentzian polynomials, polynomial capacity, and related methods in the geometry of polynomials. The archived materials below collect the assignments and lecture notes from the course.
Assignments
Homework 1
Interlacing polynomials, stability preservers, and related foundations.
Homework 2
Exercises continuing the development of Lorentzian and capacity techniques.
Homework 3
Non-homogeneous polynomials and capacity bounds.
Lecture notes
The lecture notes are kept in the original sequence, with a separate note for the Heron–Rota–Welsh theorem.
Lectures 1–7
Opening material and basic polynomial tools.
Lectures 8–11
Further development of the Lorentzian framework.
Lectures 12–13
Capacity and intermediate applications.
Lectures 14–21
Later lectures and applications.
Heron–Rota–Welsh theorem
A focused note on the Heron–Rota–Welsh theorem in the language of Lorentzian polynomials.