Ringvorlesung
- Bernd Sturmfels
- Melchior Wirth
- Bian Wu
Abstract
Part I: Bernd Sturmfels
Convex Polytopes
The sources are the two books:
- Rekha Thomas: Lectures in Geometric Combinatorics, American Mathematical Society, 2006
- Guenter Ziegler: Lectures on Polytopes, Springer Verlag, 1995
The lectures are mostly based on [Thomas]. For additional reading, [Ziegler] is recommended. The library provides both e-books and hard copies.
Each lecture is broken into two parts, with a short break in between. Here is a detailed syllabus:
- October 20: 9:30 The Main Theorem [Thomas, Chapter 2]; 10:15 Faces of Polytopes [Thomas, Chapter 3]
- October 27: 9:30 Schlegel Diagrams [Thomas, Chapter 4]; 10:15 Steinitz' Theorem [Ziegler, Chapter 4]
- November 10: 9:30 Gale Diagrams [Thomas, Chapters 5 and 6]; 10:15 The Upper Bound Theorem [Ziegler, Section 8.4]
- November 17: 9:30 Triangulations [Thomas, Chapter 7]; 10:15 The Secondary Polytope [Thomas, Chapter 8]
Exercise session will be organized spontaneously. Computations are strongly encouraged. Try OSCAR.
Part II: Melchior Wirth
Title: Quantum Optimal Transport
Following the success of optimal transport across applied and pure mathematics, in recent years a theory of quantum optimal transport has started to evolve. After a brief overview of classical optimal transport theory from an algebraic point of view, we will introduce some concepts of quantum measure theory and quantum information. We will then discuss various quantum Wasserstein metrics, in particular coupling-based and dynamical distances, and see some applications in the analysis of open quantum systems.
Date and time: November 24, December 1, 8, 15. tbc
Part III: Bian Wu
Date and time: tba
Date and time info
Monday 9:30-11:00
Keywords
Convex Polytopes
Recorded lecture
-
Convex Polytopes I
Bernd Sturmfels -
Convex Polytopes II
Bernd Sturmfels -
Convex Polytopes III
Bernd Sturmfels -
Convex Polytopes IV
Bernd Sturmfels -
Quantum Optimal Transport I
Melchior Wirth -
Quantum Optimal Transport II
Melchior Wirth -
Quantum Optimal Transport III
Melchior Wirth -
Quantum Optimal Transport IV
Melchior Wirth -
Asymptotic Methods in Oscillation Problems I
Bian Wu -
Asymptotic Methods in Oscillation Problems II
Bian Wu -
Asymptotic Methods in Oscillation Problems III
Bian Wu
