MenuEvents for 04/12/2019 from all calendars
Working Seminar on Quantum Groups
Time: 10:30AM - 12:00PM
Location: BLOC 624
Speaker: Priyanga Ganesan, TAMU
Title: Modular properties of the Haar state
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:50PM
Location: BLOC 628
Speaker: Dr. Lennie Friedlander, University of Arizona
Title: The Dirichlet-to-Neumann operator for quantum graphs
Abstract: TBA
Algebra and Combinatorics Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 628
Speaker: Michael Brannan, Texas A&M University
Title: Hopf algebras and non-local games
Abstract: A non-local game consists of two players, who are each provided questions from a referee and then supply answers. The game comes with rules which determine if the answers supplied by the players are correct or not. The players cooperate to win each round of the game, but the ``non-locality'' of the game means that the players cannot communicate by classical means during each round of the game. They can, however, agree upon a shared strategy for producing satisfactory answers. Non-local games are of interest in quantum information theory because quite often the only winning strategy is a so-called quantum strategy - i.e., one which utilizes some shared resource of quantum entanglement between the players. In this talk, I will focus on a particular class of non-local games, called synchronous games. For these games one can associate to a game an associative algebra A whose structure completely characterizes the existence of winning deterministic and probabilistic (quantum) strategies for these games. As a particular example, I will focus on the graph isomorphism game, which takes as inputs two graphs, and is devised so that a winning deterministic strategy requires that the two graphs be isomorphic. On the other hand, a probabilistic winning strategy relaxes this condition to the two graphs being what quantum information theorists call ``quantum isomorphic''. I will explain how the notion of quantum isomorphism mentioned above is intimately connected to the theory of Hopf bi-Galois objects: Two graphs are quantum isomorphic if and only if the game algebra A is a Hopf bi-Galois extension over the universal Hopf algebras coacting on the function algebras of the two graphs. I will explain how this Hopf-algebraic interpretation of the graph isomorphism game provides some fundamental new insights. **NOTE**: There will be a sequel to this talk given by Kari Eifler (TAMU) at 4pm in the Linear Analysis Seminar. Both talks will be complementary, yet self-contained.
Student Working Seminar in Groups and Dynamics
Time: 3:00PM - 4:00PM
Location: BLOC 506A
Speaker: Amanda Hoisington
Title: Coarse embeddings under group extensions
Abstract: I will be going over a paper by Arzhantseva and Tessera (2017) which proves, by construction, that admitting a coarse embedding into Hilbert space is not preserved under group extension."
Linear Analysis Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Kari Eifler, TAMU
Title: The graph isomorphism game for quantum graphs
Abstract: Non-local games give us a way of observing quantum behaviour through the observation of only classical data, and there are several different mathematical models to consider. The graph isomorphism game is one such game and we say two graphs are quantum isomorphic if there is a winning quantum strategy for the graph isomorphism game. We show that if a pair of (quantum) graphs X and Y are algebraically quantum isomorphic then the quantum automorphism groups G_X and G_Y are monodially equivalent. We also show a converse: if a compact quantum group G is monodially equivalent to G_X, then G is isomorphic to G_Y for a quantum graph Y. **NOTE**: This talk will be immediately preceded the Algebra and Combinatorics Seminar, where Michael Brannan (TAMU) will introduce non-local games and related algebraic structures. The subject material of both talks will be complementary. Attendance in both talks is therefore highly encouraged, although both talks will be self-contained.
Geometry Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 628
Speaker: David Ben-Zvi, UT Austin
Title: Integrating quantum hamiltonians
Abstract: Harish Chandra showed that symmetric spaces carry large commutative algebras of invariant differential operators, generalizing the Laplacian. The symbols of these differential operators provide the commuting Hamiltonians responsible for many classical integrable systems. I'll describe joint work with Sam Gunningham (arXiv/1712.01963) describing a universal ``integration" for these classical and quantum Hamiltonian systems, through a categorical analog of the Harish-Chandra isomorphism, constructed via the geometric Langlands correspondence.
