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Seminars and Colloquiums
for the week of September 25, 2017


Adam Spannaus, UTK, Tuesday
Deniz Stiegemann, Institut of Theoretical Physics, Leibniz Universität Hannover, Wednesday
Thomas Weighill,UTK, Wednesday
Wenyu Lei, Texas A&M University, Wednesday
Theodora Bourni, UTK, Thursday
Tadele Mengesha, UTK, Friday

3:00 pm – 3:30 pm
Monday, Tuesday, Wednesday
Ayres 401
Hosted By: Kelly Buch

Tuesday, September 26th

TITLE:           Bayesian Point Set Registration
SPEAKER:    Adam Spannaus (UTK)
TIME:            2:10-3:25P
ROOM:         Ayres 113      
The promise that High Entropy Alloys hold for society is large, but our current understanding is limited by few theoretical results. At the nanoscale researchers use Atomic Probe Tomography to deduce the chemical ordering and lattice structure of these alloys. This data however, is corrupted by noise and having up to 67% of the data missing.

In this talk, we will describe the mathematics necessary to find the correct alignment and positioning between these sparse and noisy data sets and the true configuration. We will derive the statistical model describing Bayesian Point Set Registration and show through numerical examples how Monte Carlo Markov Chain methods can be used to solve this problem.

This work is ongoing research with Professors Maroulas and Keffer (Materials Science: UTK) and Kody Law (ORNL and UTK).

Wednesday, September 27th

Title:            Dynamics for holographic codes
Speaker:      Deniz Stiegemann, Institut of Theoretical Physics, Leibniz Universität Hannover
Time:           2:30-3:20p
Room:         Ayres 113
We describe how to introduce dynamics for the holographic states and codes introduced by Pastawski, Yoshida, Harlow and Preskill. This task requires the definition of a continuous limit of the kinematical Hilbert space of a finite H which we argue may be achieved via the semicontinuous limit of Jones. Dynamics is then introduced by building a unitary representation of a group known as Thompson's group T, which is closely related to the conformal group conf(R^{1,1}). The bulk Hilbert space is then realised as a special subspace of the semicontinuous limit H spanned by a class of distinguished states which can be assigned a discrete bulk geometry. The analogue of the group of large bulk diffeomorphisms is then given by a unitary representation of the Ptolemy group Pt, on the bulk Hilbert space thus realising a toy model of AdS/CFT which we call the Pt/T correspondence. This paper is primarily targeted at physicists, particularly, quantum information theorists, however mathematicians knowledgeable of circle groups and Thompson's groups F and T may find the paper helpful as a way to get a sense of the AdS/CFT correspondence.

TITLE:           Group actions and the maximal Roe algebra II
SPEAKER:    Thomas Weighill, UTK
TIME:            3:35-4:25p
ROOM:         Ayres 405      
The (maximal) Roe algebra is an important C*-algebra which appears in the index theory of non-compact complete Riemannian manifolds. It is also a coarse invariant, and so is naturally an object of study in coarse geometry. In a previous talk, we saw what it means for a group to act on a metric space by coarse equivalences and introduced a kind of "coarse quotient" which we call X_G. In this talk, we will begin to establish a relationship between the maximal Roe algebras of X and X_G for certain kinds of group action. This correspondence will involve the (full) crossed product of the Roe algebra with the group G. We will introduce all the necessary concepts from the theory of C* algebras, and recall the definition of the Roe algebra and its maximal version. This is joint work with Logan Higginbotham.

TITLE:            Numerical Approximation of the Integral Fractional Laplacian
SPEAKER:     Wenyu Lei, Texas A&M University
TIME:             3:35-4:35p
ROOM:           Ayres 113   
We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the integral fractional Laplacian. We first derive an integral representation of the bilinear form corresponding to the variational problem. The numerical approximation of the action of the corresponding stiffness matrix consists of three steps: (i) apply a sinc quadrature scheme to approximate the integral representation by a finite sum where each term involves the solution of an elliptic partial differential equation defined on the entire space, (ii) truncate each elliptic problem to a bounded domain,  (iii) use the finite element method for the space approximation on each truncated domain. We first discuss the consistency error for the three steps together with the numerical implementation of the entire algorithm. Then we provide an error estimate between the solution and its approximation in the energy norm. (Joint work with Andrea Bonito and Joseph Pasciak).

Thursday, September 28th

TITLE:          Ancient Pancakes II
SPEAKER:   Theodora Bourni, UTK
TIME:           5:00pm - 6:00pm
ROOM:        Ayres 113
We continue our proof from last week that, up to rigid motions, there is a unique compact, convex, rotationally symmetric, ancient solution of mean curvature flow that lies in a slab of width $\pi$ and in no smaller slab. This is joint work with Mat Langford and Giuseppe Tinaglia.

Friday, September 29th

TITLE:            The analysis of a function space associated with peridynamics 
SPEAKER:     Tadele Mengesha
TIME:             3:30-4:30pm
ROOM:           Ayres 405
In this talk I will present recent results on some functional analytic properties of a function space related to a nonlocal model in mechanics called peridynamics.

The nonlocal model is made up of a coupled system of integral equations.  Via variational analysis well posedness of the nonlocal system subject to (potentially volumetric) constraints will be demonstrated. The main focus will be the associated energy spaces and their connections with classical function spaces. Conditions that imply compact embedding of these spaces in Lp spaces will be given. Using a fractional Hardy-type inequality, we also establish equivalence of some of these spaces with classical fractional Sobolev spaces. Open problems related to these function spaces and their connection in proving regularity of solutions to systems of integral equations will be discussed.

If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.

If you have questions, or a date you would like to confirm, please contact colloquium AT math DOT utk DOT edu

Past notices:






last updated: September 2017

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