Seminars and Colloquiums
for the week of February 20, 2017
Thomas Weighill, UTK, Monday
Joshua Mike, UTK, Tuesday
Remus Nicoara, UTK, Tuesday
Marta D'Elia, Sandia National Lab, Wednesday
Mike Langston, Prof in Electrical Engineering and Computer Science, UTK, Thursday
TEA TIME -
3:00 pm – 3:30 pm
Monday; Room: Ayres 4th Floor Common Area
Tuesday & Wednesday; Room: Ayres 401
Monday, February 20th
TITLE: Coarse neighbourhoods and hybrid large scale normal spaces II
SPEAKER: Thomas Weighill, UTK
TIME: 2:30pm – 3:20pm
ROOM: Ayres 113
Last time, we proved a general form of Urysohn's Lemma and the Tietze Extension Theorem in terms of neighbourhood operators. In this talk we introduce hybrid large scale normal spaces and state the corresponding results for these spaces. We then look at some examples and properties of hybrid large scale normal spaces, and discuss some applications to the Higson corona. This is joint work with J. Dydak.
Tuesday, February 21st
TITLE: Constructing Distributions of Persistence Diagrams: Part I
SPEAKER: Joshua Mike, UTK
TIME: 2:10pm – 3:25pm
ROOM: Ayres 113
We begin with background on the pipeline of persistent homology for point cloud data, including filtrations of simplicial complexes and describing how to build topological summaries (including persistence diagrams) from the filtration. Examples will be provided to motivate use in data analysis. We will discuss the issues which must be overcome to construct a (data oriented) kernel distribution of persistence diagrams.
In Part II we will introduce the machinery necessary for building these distributions, show some examples, and discuss future directions.
Wednesday, February 22nd
TITLE: Analytic deformations of commuting squares
SPEAKER: Dr. Remus Nicoara, UTK
ROOM: Ayres 113
Finite groups, and more generally finite dimensional Hopf C*-algebras, can be encoded in S.Popa’s commuting squares and thus used as construction data for V.Jones’ subfactors. We construct analytic deformations of such commuting squares, and present consequences to the theory of complex Hadamard matrices and the theory of subfactors.
Thursday, February 23rd
DIFFERENTIAL EQUATIONS SEMINAR
TITLE: A coupling strategy for nonlocal and local models with applications to static peridynamics and classical elasticity
SPEAKER: Marta D'Elia, Sandia National Lab
ROOM: Ayres 113
The use of nonlocal models in science and engineering applications has been steadily increasing over the past decade. The ability of nonlocal theories to accurately capture effects that are difficult or impossible to represent by local Partial Differential Equation (PDE) models motivates and drives the interest in this type of simulations. However, the improved accuracy of nonlocal models comes at the price of a significant increase in computational costs compared to, e.g., traditional PDEs. In particular, a complete nonlocal simulation remains computationally untenable for many science and engineering applications.
As a result, it is important to develop local-to-nonlocal coupling strategies, which aim to combine the accuracy of nonlocal models with the computational efficiency of PDEs. The basic idea is to use the more efficient PDE model everywhere except in those parts of the domain that require the improved accuracy of the nonlocal model.
We develop and analyze an optimization-based method for the coupling of nonlocal and local problems in the context of nonlocal elasticity. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. We prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia's agile software components toolkit.
Numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method; these numerical tests provide the groundwork for the development of efficient and effective engineering analysis tools. As an application, we present results for the coupling of static peridynamics and classical elasticity.
TITLE: Discovering Latent Relationships in Highly heterogeneous Data: Mathematical Methods, Scalable Algorithms and Life Science Applications
SPEAKER: Mike Langston, Prof in Electrical Engineering and Computer Science, UTK
TIME: 3:40pm – 4:30pm
ROOM: Ayres 405
We will discuss the use of novel mathematical techniques such as fixed-parameter tractability in the analysis of highly inhomogeneous data. Important concerns center on noise, and the role model organisms can play in the study of human health. Critical resources include enormous repositories of emergent data, suites of novel statistical and graph theoretical methods, deep domain knowledge and high performance computing platforms. We will describe how the potential of these resources can be harnessed to help realize the promise of new strategies for the elucidation and interpretation of previously unknown relationships. Machine learning, load balancing and efficient combinatorial search can be key considerations. Examples will be drawn from a variety of biological and health science applications.
Friday, February 24th
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