Rocky Mountain Mathematical Physics Seminar

Content: The goal of this semester (Fall 2023) is to give an introduction to the
Mathematics of Quantum Entanglement and the Geometric Phase.
Organizer: Markus Pflaum and Sheagan John
Hours and Venue: Wednesday 3:30 p.m. - 4:20 p.m., MATH 350
Online Option: Meeting ID: 940 0255 3301 (for the Passcode please contact the organizers)
Topics and talks:
  • An Introduction to C*-Algebras and their state spaces (Markus Pflaum, Sep 20)
  • Hilbert-Schmidt operators and density matrices (Sheagan John, Sep 27)
  • Partial traces (Connor McCranie, Oct 4)
  • Completely positive maps and Stinespring’s theorem (Daniel Spiegel, Oct 11)
  • Stratification of spaces of density matrices (Howy Jordan, Oct 18)
  • The geometric phase phase à la M. Berry (Mert Okyay, Nov 1)
  • The Bures metric and Uhlman's connection (Ezzedine El Sai, Nov 8)
  • Entangelement and invariant theory (Joshua Groshow)
Literature
(with annotations):
  • Online Resources on mathematical foundations and geometric quantum mechanics:

    • Pflaum, M.J., The Geometry of Classical and Quantum Fields.

    The FANCY Project on Functional Analysis and Noncommutative Geometry.

    The CRing Project on Commutative Algebra and related topics.

    Takhtajan, L.A., Quantum Mechanics for Mathematicians, AMS (2008).

    Manny: Advanced mathematical treatment, not self-contained. Sometimes not as explanatory as I would have liked. I couldn't determine the general formulation of classical graded (super) mechanics from the chapter on this topic.