ABSTRACT: The spectral propinquity is a distance over the class of metric spectral triples, up to unitary equivalence. It is constructed as a special form of the propinquity between compact quantum metric spaces, itself rooted in the work on the Gromov-Hausdorff distance and its noncommutative analogues, in the more general framework of Rieffel's work in noncommutative metric geometry. In this talk, we wish to present the spectral propinquity and discuss various properties and examples of convergence in the sense of this metric: for instance, we will discuss how the spectrum of Dirac operators is continuous with respect to the spectral propinquity, and how various spectral triples on quantum tori, quantum solenoids, and Bunce-Deddens algebras are limits of other spectral triples.
The spectral propinquity
Sep. 19, 2024 3:35pm (MATH 3…
Probability
Mei Yin (University of Denver)
X
We give a survey into parking functions, concentrating in particular on the probabilistic and combinatorial aspects. Joint work with multiple collaborators: Irfan Durmi\'{c}, Alex Han, Pamela E. Harris, Rodrigo Ribeiro; Richard Stanley; Stephan Wagner.
Parking functions: probabilistic and combinatorial
Sep. 19, 2024 4:45pm (MATH 3…
Grad Student Seminar
Ezzeddine El Sai (CU Boulder)
X
The Yang–Mills existence and mass gap problem is one of the Millennium Prize problems and a central problem in mathematical physics. In this talk, we will discuss the statement of the problem and unravel what it means. We will also discuss connections with geometry, analysis, and probability.
The spectral propinquity