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Events for December 1, 2017 from General and Seminar calendars

Working Seminar in Orbit Equivalence and Measured Group Theory

Time: 09:30AM - 10:30AM

Location: BLOC 605AX

Speaker: Konrad Wrobel

Title: Stable Actions and Central Extensions III

Abstract: I will verify the stability of the action constructed in the last talk by Mehrzad.

Working Seminar on Quantum Computation and Quantum Information

Time: 10:30AM - 11:30PM

Location: BLOC 628

Speaker: Ken Dykema, TAMU

Title: Non-closure of a set of quantum correlations.

Abstract: Using elementary techniques, we show that the convex set C_q(5,2) of quantum correlations with 5 inputs and 2 outputs is not closed. (Joint work with Vern Paulsen and Jitendra Prakash).

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Mahmood Ettehad, Texas A&M University

Title: Network graph reconstruction from path correlations (joint with Inverse Problems Seminar)

Abstract: Routing network can be modeled by a connected graph with a set of boundary vertices where the measurements can be taken. Among the possible measurements are the transmission times between any pair of boundary vertices. Furthermore, it has been observed that the correlation between transmission times along two paths can be used as a proxy for the length of the intersection of the paths. The aim is to use this information to solve the problem of network tomography (reconstruct the structure of the entire network together with the length of all links).
Mathematically, given an edge-weighted graph we can measure the weight of the segment common to any two paths A-Z and B-Z, where A, B and Z are boundary vertices. We will present a necessary and sufficient condition for the graph to be reconstructable from this information, and will describe the reconstruction algorithm.
Based on a joint work with Gregory Berkolaiko and Nick Duffield (ECE TAMU).

Inverse Problems Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Mahmood Ettehad, Texas A&M University

Title: Network graph reconstruction from path correlations (Joint with Math Physics and Harmonic Analysis seminar))


Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 117

Speaker: Carlos Arreche, UT Dallas

Title: Projectively integrable linear difference equations and their Galois groups

Abstract: To a linear difference system S is associated a differential Galois group G that measures the differential-algebraic properties of the solutions. We say S is integrable if its solutions also satisfy a linear differential system of the same order, and we say S is projectively integrable if it becomes integrable “modulo scalars”. When the coefficients of S are in C(x) and the difference operator is either a shift, q-dilation, or Mahler operator, we show that if S is integrable then G is abelian, and if S is projectively integrable then G is solvable. As an application of these results one can show certain generating functions arising in combinatorics satisfy no algebraic differential equations. This is joint work with Michael Singer.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Jose Rodriguez, University of Chicago

Title: Numerical computation of Galois groups and braid groups

Abstract: Galois groups are an important part of number theory and algebraic geometry. To a parameterized system of polynomial equations one can associate a Galois group whenever the system has k (finitely many) nonsingular solutions generically. This Galois group is a subgroup of the symmetric group on k symbols. Using random monodromy loops it has already been shown how to compute Galois groups that are the full symmetric group. In the first part of this talk, we show how to compute Galois groups that are proper subgroups of the full symmetric group. We give examples from formation shape control and algebraic statistics. In the second part, we discuss the generalization to braid groups. Braid groups were first introduced by Emil Artin in 1925 as a generalization of the symmetric group and have more refined information than the Galois group. We develop algorithms to compute a set of generators for these groups using homotopy continuation. We conclude with an implementation using Bertini.m2, an interface to the numerical algebraic geometry software Bertini through Macaulay2. This is joint work with Jonathan Hauenstein and Frank Sottile and with Botong Wang.

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Li Gao, University of Illinois at Urbana-Champaign

Title: Entropic uncertainty relations via Noncommutative Lp Spaces

Abstract: The Heisenberg uncertainty principle states that it is impossible to prepare a quantum particle for which both position and momentum are sharply defined. Entropy is a natural measure of uncertainty. The first entropic formulation of the uncertainty principle was proved by Hirschman and since then entropic uncertainty relations have been obtained for many different scenarios, including some recent advances on uncertainty relations with quantum memory. In this talk, I will present an approach to entropic uncertainty relations via noncommutative Lp norms. We show that the natural connection between noncommutative Lp Spaces and Renyi information measure gives certain uncertainty relation for two complementary subalgebras of a tracial von Neumann algebra. This is a joint work with Marius Junge and Nicholas LaRacuente.