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Texas A&M University
Mathematics

Events for 03/08/2019 from all calendars

Numerical Analysis Seminar

iCal  iCal

Time: 12:45PM - 1:45PM

Location: BLOC 628

Speaker: Sara Pollock, University of Florida

Title: Anderson acceleration improves the convergence rate in linearly converging fixed point methods

Abstract: The extrapolation method known as Anderson acceleration has been used for decades to speed up nonlinear solvers in many applications, however a mathematical justification of the improved convergence rate has remained elusive. Here, we provide theory to establish the improved convergence rate. The key ideas of the analysis are relating the difference of consecutive iterates to residuals based on performing the inner-optimization in a Hilbert space setting, and explicitly defining the gain in the optimization stage to be the ratio of improvement over a step of the unaccelerated fixed point iteration. The main result we prove is that this method of acceleration improves the convergence rate of a fixed point iteration to first order by a factor of the gain at each step.


Mathematical Physics and Harmonic Analysis Seminar

iCal  iCal

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Dr. Selim Sukhtaiev, Rice University

Title: Localization for Anderson Models on Metric and Discrete Tree Graphs

Abstract: In this talk I will discuss spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional energies. All results are proved under the minimal hypothesis on the type of disorder: the random variables generating the trees assume at least two distinct values. This level of generality, in particular, allows us to treat radial trees with disordered geometry as well as Schr\"odinger operators with Bernoulli-type singular potentials. This is based on joint work with D. Damanik and J. Fillman. JOINT WITH THE GROUPS AND DYNAMICS SEMINAR


Groups and Dynamics Seminar

iCal  iCal

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Sr. Selim Sukhtaiev, Rice University

Title: Localization for Anderson Models on Metric and Discrete Tree Graphs

Abstract: In this talk I will discuss spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional energies. All results are proved under the minimal hypothesis on the type of disorder: the random variables generating the trees assume at least two distinct values. This level of generality, in particular, allows us to treat radial trees with disordered geometry as well as Schr\"odinger operators with Bernoulli-type singular potentials. This is based on joint work with D. Damanik and J. Fillman. [Note: this is a joint seminar with the Mathematical Physics and Harmonic Analysis Seminar]


Algebra and Combinatorics Seminar

iCal  iCal

Time: 3:00PM - 3:50PM

Location: BLOC 628

Title:


Student Working Seminar in Groups and Dynamics

iCal  iCal

Time: 3:00PM - 4:00PM

Location: BLOC 506A

Speaker: Krzysztof Święcicki

Title: Some remarks on FLp actions

Abstract: I will discuss property FLp - an analog of property (T). I'll sketch an argument that property (T) implies measure preserving property FLp. Based on a work in progress with Alan Czuron.


Geometry Seminar

iCal  iCal

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Giuseppe Martone, University of Michigan

Title: Hitchin representations and positive configurations of apartments

Abstract: Hitchin singled out a preferred component in the character variety of representations from the fundamental group of a surface to PSL(d,R). When d=2, this Hitchin component coincides with the Teichmuller space consisting of all hyperbolic metrics on the surface. Later Labourie showed that Hitchin representations share many important differential geometric and dynamical properties. Parreau extended previous work of Thurston and Morgan-Shalen to a compactification of the Hitchin component whose boundary points are described by actions of the fundamental group of the surface on a building. In this talk, we offer a new point of view for the Parreau compactification, which is based on certain positivity properties discovered by Fock and Goncharov. Specifically, we use the Fock-Goncharov construction to describe the intersection patterns of apartments in invariant subsets of the building that arises in the boundary of the Hitchin component.