Events for 10/08/2021 from all calendars
Working Seminar on Banach and Metric Spaces
Time: 1:00PM - 3:00PM
Location: BLOC 302
Speaker: Florent Baudier, Texas A&M University
Title: The geometry of Hamming graphs: non-embeddability
Noncommutative Geometry Seminar
Time: 2:00PM - 3:00PM
Location: ZOOm
Speaker: Benjamin Steinberg, City College of New York and CUNY Graduate Center
Title: Cartan pairs of algebras
Abstract: In the seventies, Feldman and Moore studied Cartan pairs of von Neumann algebras. These pairs consist of an algebra A and a maximal commutative subalgebra B with B sitting “nicely” inside of A. They showed that all such pairs of algebras come from twisted groupoid algebras of quite special groupoids (in the measure theoretic category) and their commutative subalgebras of functions on the unit space, and that moreover the groupoid and twist were uniquely determined (up to equivalence). Kumjian and Renault developed the C*-algebra theory of Cartan pairs. Again, in this setting all Cartan pairs arise as twisted groupoid algebras, this time of effective etale groupoids, and again the groupoid and twist are unique (up to equivalence). In recent years, Matsumoto and Matui exploited that for directed graphs satisfying Condition (L), the corresponding graph C*-algebra and its commutative subalgebra of functions on the path space of the graph form a Cartan pair to give C*-algebraic characterizations of continuous orbit equivalence and flow equivalence of shifts of finite type. The key point was translating these dynamical conditions into groupoid language. Since the Leavitt path algebra associated to a graph is the “Steinberg” algebra of the same groupoid, this led people to wonder about whether these dynamical invariants can be read off the pair consisting of the Leavitt path algebra and its subalgebra of locally constant maps on the path space. The answer is yes and it turns out in the algebraic setting, one doesn’t even need Condition (L). Initially work was focused on recovering an ample groupoid from the pair consisting of its “Steinberg” algebra and the algebra of locally constant functions on the unit space. But no abstract theory of Cartan pairs existed and twists had not yet been considered. Our work develops the complete picture. This is joint work with Becky Armstrong, Gilles G. de Castro, Lisa Orloff Clark, Kristin Courtney, Ying-Fen Lin, Kathryn McCormick, Jacqui Ramagge and Aidan Sims
URL: Event link
Algebra and Combinatorics Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 302
Speaker: Roberto Palomares, TAMU
Title: Q-systems and higher unitary idempotent completion for C* 2-categories
Abstract: A Q-system is a unitary version of a Frobenius algebra object in a tensor category or a C* 2-category. Q-systems were introduced by Longo to characterize the canonical endomorphism of a finite index inclusion of infinite von Neumann factors. Following work of Douglass-Reutter, a Q-system is also a unitary version of a higher idempotent. We will define a higher unitary idempotent completion for C* 2-categories called Q-system completion, and describe some of its properties and examples. We will show that C*Alg, the C* 2-category of right correspondences of unital C*-algebras is Q-system complete by adapting a technique from subfactors theory called realization. This result allows for the straightforward adaptation of subfactor results to C*-algebras, characterizing finite Jones-Watatani-index extensions of unital C*-algebras $A \subset B$ equipped with a faithful conditional expectation $E:B \to A$ in terms of the Q-systems in C*Alg.
Geometry Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 302
Speaker: F. Holweck, U. Belfort/Auburn
Title: Graph states and the variety of principal minors for binary symmetric matrices.
Abstract: Abstract: Graph states are special types of quantum states well studied in quantum information theory for their potential applications to quantum error correcting codes or measurement-based quantum computing. The variety of principal minors is an algebraic variety introduced by Holz and Strumfels to study the relations among principal minors of matrices. Its study also has applications to various fields such as matrix theory, probability, and computer vision. In this talk I will explain how one can build a correspondence between the graph states classification under the so-called local Clifford group and the orbits of the variety of principal minors for symmetric matrices over the 2-elements field. This is joint work with Vincenzo Galgano (Trento Univ).