Organizers: Nguyễn Đăng Khải Hoàn, Lê Minh Trí.
Time: 8:00 pm, from Saturday, August 24, 2024.
Place: Online via Zoom. Contact me for the link and further concerns.
Goal: This is a seminar for our working group on mixed volume and related topics. We will discuss several aspects and questions on mixed volume and its relation with other fields of mathematics.
We will cover the following topics:
Volume and mixed volume: basic facts.
Brunn--Minkowski and Alexandrov--Frenchel inequalities.
The equality cases of Alexandrov--Frenchel inequalities.
Bernstein's theorem.
Lorentzian polynomials.
Mixed multiplicities.
Nonnegative forms with sublevel sets of minimal volume, Khazhgali Kozhasov & Jean Bernard Lasserre.
Convex Bodies: The Brunn–Minkowski Theory, Rolf Schneider.
Introduction to Geometric Probability, Daniel A. Klain & Gian-Carlo Rota.
The extremals of the Alexandrov–Fenchel inequality for convex polytopes, Yair Shenfeld & Ramon van Handel.
Solving Systems of Polynomial Equations, Bernd Sturmfels.
Lorentzian polynomials, Petter Brändén & June Huh.
Convex bodies and graded families of monomial ideals, Yairon Cid-Ruiz & Jonathan Montaño.