| Date: | October 4, 2019 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | Jurij Volcic, TAMU |
| Title: | Noncommutative polynomials describing convex sets |
| Abstract: | The free semialgebraic set D determined by a hermitian noncommutative
polynomial f is the set of tuples of hermitian matrices X such that f(X)
is positive semidefinite. When f is a hermitian monic linear pencil, D
is called a free spectrahedron. Since it is the feasible set of a linear
matrix inequality (LMI), it is evidently convex. Conversely, it is
well-known that every convex free semialgebraic set is a free
spectrahedron. This talk presents a solution to the basic problem of
determining those noncommutative polynomials f for which D is convex. A
consequence is an effective probabilistic algorithm that not only
determines if D is convex, but also produces its LMI representation.
Further results address 1x1 noncommutative polynomials describing convex
sets. |
|
| Date: | October 18, 2019 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | Li Gao, TAMU |
| Title: | Quantum entropy and noncommutative L_p norms |
| Abstract: | Entropy and its variants play a central role in both classical- and quantum information theory. In last decade, the connection between quantum entropies and noncommutative $L_p$-norms has found many application in quantum information. In this talk, I will explain how this connection provides functional analytic tools to entropic quantity, such as quantum channel capacity and entropic uncertainty principle. A new connection between relative entropy and subfactor index will also be mentioned. This talk is based on joint works with Marius Junge and Nicholas LaRacuente.
|
|
| Date: | October 25, 2019 |
| Time: | 4:00pm |
| Location: | BLOC 628 ** |
| Speaker: | Jordyn Harriger, Indiana University |
| Title: | Planar Algebras Related to the Symmetric Groups |
| Abstract: | THIS IS A JOINT SEMINAR WITH GEOMETRY, ALGEBRA & COMBINATORICS |
|
| Date: | November 22, 2019 |
| Time: | 4:00pm |
| Location: | BLOC 624 *** |
| Speaker: | Priyanga Ganesan, TAMU |
| Title: | Quantum Majorization in Infinite Dimensions |
| Abstract: | Majorization is a concept from linear algebra that is used to compare disorderness in physics, computer science, economics and statistics. Recently, Gour et al (2018) extended matrix majorization to the quantum mechanical setting to accommodate ordering of quantum states. In this talk, I will discuss a generalization of their definition and entropic characterization of quantum majorization to the infinite dimensional setting, using operator space tensor products and duality. This is based on joint work with Li Gao, Satish Pandey and Sarah Plosker. |
|
| Date: | December 4, 2019 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Miza Rahaman, University of Waterlooo |
| Title: | Bisynchronous Games and Factorizable Maps |
| Abstract: | In the theory of non-local games, the graph isomorphism game stands
out to be an intriguing one. Specially when the algebra of this game
is considered. This is because this game establishes a close connection
between the algebra of the game and the theory of quantum permutation
groups. It turns out that the graph isomorphism game is an example
of a bisynchronous game. In this talk, I will introduce these games and
the corresponding correlations arising from the perfect strategies for such
games. Moreover, when the number of inputs is equal to the number of
outputs, each bisynchronous correlation gives rise to a completely positive
map which will be shown to be factorizable in the sense of Haagerup-
Musat. This is a joint work with Vern Paulsen. |
|
| Date: | December 6, 2019 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | Chris Phillips, University of Oregon |
| Title: | The Cuntz semigroup of the crossed product by a finite group action with the weak tracial Rokhlin property |
| Abstract: | Let A be a simple unital C*-algebra. Suppose that a finite group G acts on A, and that the action has the weak tracial Rokhlin property, a generalization of the Rokhlin property which uses positive elements instead of projections, and is fairly common. We prove that, after discarding the classes of the nonzero projections, the Cuntz semigroup of the fixed point algebra is just the fixed points in the Cuntz semigroup of A. For context, for algebras without strict comparison, the Cuntz semigroup is often very hard to compute. As a corollary, we prove that the radius of comparison of the crossed product satisfies rc (C^* (G, A)) \leq [1 / card (G)] rc (A). We also give an example of a simple separable unital AH algebra A and an action of the two element group G on A which has the Rokhlin property, and such that rc (A) and rc (C^* (G, A)) are both strictly positive. The way the weak tracial Rokhlin property is used in the proof is different from the usual methods in C*-algebras. Joint work with M. Ali Asadi-Vasfi and Nasser Golestani. |
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