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Seminars and Colloquiums
for the week of October 12, 2015


Brian Allen, UTK, Monday
Kate Thompson, Davidson College, Monday
Samy Tindel, Purdue University, Tuesday
Ahmed Khamayseh, Palestine Polytechnic University, Tuesday
Kertesha Riley UTK, Center for Career Development, Wednesday
Cheng Wang, University of Mass, Dartmouth, Wednesday

Tea Time, Monday - Wednesday, 3:00 pm
Hosted by Khoa Dinh

Monday October 12

TITLE: Non-Compact Inverse Mean Curvature Flow in Euclidean Space
TIME: 2:30 – 3:20pm
ROOM: Ayres 114
SPEAKER: Brian Allen, UTK
ABSTRACT: Inverse Mean Curvature Flow (IMCF) is an important geometric evolution equation that has been used to prove interesting geometric inequalities, most notably the Riemannian Penrose Inequality from General Relativity. In this talk we will discuss my result of long time existence of IMCF for bounded graphs over cylinders and explore the asymptotic properties we expect for the flow.

TITLE: The sum of four squares over real quadratic number fields.
TIME: 3:35 – 4:25pm
ROOM: Ayres 114
SPEAKER: Kate Thompson, Davidson College
ABSTRACT: That the sum of four squares represents all positive integers is a well-known and celebrated result–there even is a formula for the number of represented (often presented in undergraduate number theory classes). What happens in the number field analogue? Using Siegel’s theory of local densities and Hilbert modular forms, we will answer this question in the case of real quadratic number fields. This includes providing explicit (and, on occasion, sharp) bounds on the Eisenstein coefficients of the associated theta series.

Tuesday October 13

TITLE: Drift estimation for differential equations driven by fractional Brownian motions
TIME: 2:10 -3:25pm
ROOM: Ayres 114
SPEAKER: Samy Tindel, Purdue University
ABSTRACT: : We focus in this talk on statistical problems for noisy differential equations driven by an additive fractional Brownian motion, either in a 1-d or general d-dimensional context. I will first review the standard procedures in order to estimate the Hurst parameter, the diffusion coefficient and finally the drift coefficient of the equation. Then I will give an account on two new results in this direction:
(1) A new class of estimators in ergodic situations, when the dependence of the drift with respect to the parameter in not linear.
(2) The LAN property for ergodic equations, which yields a lower bound for the convergence of estimators.
These results are based on some ongoing works with Eulalia Nualart (Barcelona) and Fabien Panloup (Toulouse).

TITLE: Conservative Computational Methods for Multiphysics Coupling
TIME: 3:35 – 4:35pm
ROOM: Ayres 405
SPEAKER: Ahmed Khamayseh, Palestine Polytechnic University
ABSTRACT: Multiphysics applications add a new dimension to the challenges of mesh generation and mesh adaptation. It is a common requirement in multiphysics and adaptive analysis applications to transfer solution fields and their derivative attributes between meshes and/or to other applications. While many research issues still remain in meshing methods for single-physics applications, multiphysics simulation present additional challenges that arise from the need to incorporate requirements from many, possibly tightly-coupled phenomena into the meshing process. Mapping between meshes that have different combinatorial structures is an essential part of multiscale modeling in applications where physical phenomena are measured and/or computed at different scales. We have developed and implemented mathematical tools for intermesh data transfer (or remapping) for coupled multiphysics simulation from one unstructured mesh to another, possibly topologically-distinct mesh. The Computational tools support mapping between meshes that operate with similar or dissimilar interpolation schemes. For example, mapping between a piecewise constant field (e.g. finite volume) and a piecewise linear field (e.g. finite element) will be supported. Source-to-target mappings will include: 1) volume-to-volume, 2) surface-to-surface, 3) volume-to-surface, and 4) surface-to-volume. In addition to these “mesh-to-mesh” mappings, the toolbox will accommodate mapping between mesh-based and “meshfree” (e.g. smooth particle hydrodynamics) meshes at different scales. All algorithms will provide rigorous error estimates of where the effect of the mapping is most prone to error and where the source or target mesh may need to be refined to achieve target accuracy in a user-specified norm.

Wednesday October 14

TITLE: CV and career documents workshop
TIME: 9:05 – 9:55am
ROOM: Ayres 405
SPEAKER: Kertesha Riley UTK, Center for Career Development
ABSTRACT: Kertesha Riley is the STEM Career Consultant at the UTK Center for Career Development.  This week's talk builds nicely off of last month's Professional Development Luncheon, and will focus on CVs and other career documents.  Students are encouraged to bring their CVs, resumes, and cover letters, and/or teaching and research statements with them.  Kertesha will also be back in November for an interview and job search skills talk.

TITLE: Higher order numerical schemes for the gradient flow with energy stability
TIME: 3:35 -4:35pm
ROOM: Ayres 112
SPEAKER: Cheng Wang, UMass, Dartmouth
ABSTRACT: The second order and higher order (in time) accurate numerical schemes are studied for a class of bi-stable gradient flows, such as the standard Cahn-Hilliard equation and the epitaxial thin film growth models. The convex splitting nature indicates their unique solvability and unconditional energy stability. For the second order temporal approximation, both the modified Crank-Nicholson and the backward differentiation formula (BDF) versions are considered. Moreover, a linearized approach of the nonlinear part is proposed, and the energy stability could be assured with a careful analysis. As a result of the energy stability, a sharper error estimate with an improved convergence constant available for these proposed numerical scheme. More tricky ideas could be applied to derive third order numerical schemes with a local in time convergence property. Energy stable third order numerical schemes are also under consideration.

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



last updated: May 2018

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