**Seminars and Colloquiums**

for the week of November 14, 2016

for the week of November 14, 2016

*SPEAKER:*

Ryan Jensen, UTK, Monday

Morgan Roche and Rebecca Pettit, UTK, Monday

Le Chen, University of Kansas, Tuesday

Yue Yu, Lehigh University, Wednesday

Michael Morgan Wise, UTK Thursday

Peter Perry, University of Kentucky, Thursday

Hakima Bessaih, University of Wyoming, Friday

*TEA TIME -
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401*

*Hosted by: ???*

**Monday, November 14th **

TOPOLOGY/GEOMETRY SEMINAR

TITLE: Asymptotic dimension for non-metric spaces

SPEAKER: Ryan Jensen, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres 114

Asymptotic dimension is an important coarse property. For coarse metric spaces, there are several useful definitions, which were assembled and shown to be equivalent by G. Bell and A. Dranishnikov. In this talk, we generalize some of these definitions to non-metric coarse spaces. We begin by giving some needed background information concerning coarse spaces. Next we state a definition, originally by J. Dydak and {\v{Z}}. Virk, of asymptotic dimension suitable for non-metric spaces. Finally we extend a result of J. Dydak and {\v{Z}}. Virk, which will give another definition of asymptotic dimension for non-metric spaces.

MATH BIOLOGY SEMINAR

TITLE: Discussion and Presentation of two student projects

SPEAKER: Morgan Roche and Rebecca Pettit, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres G003

** Tuesday, November 15th**

STOCHASTICS SEMINAR

TITLE: Regularity and positivity of densities for the stochastic (fractional) heat equation

SPEAKER: Le Chen, University of Kansas

TIME: 2:10pm – 3:25pm

ROOM: Ayres 114

In this talk, I will present a recent study on the density of the solution to a semilinear stochastic (fractional) heat equation (SHE), which includes the parabolic Anderson model as a special case. In the first part, we prove that the solution to a semilinear SHE with measure-valued initial data has a smooth joint density at multiple points. This result extends the work by Mueller and Nualart [EJP'08] from the density at single point to the joint density at multiple points and from function-valued initial data to more general initial data. This is achieved by proving that solutions to a related stochastic partial differential equation have negative moments of all orders. In the second part, we establish the strict positivity of the density in the interior of the support of the joint law. This result extends the known results to allow measure-valued initial data and unbounded diffusion coefficient.

This talk is based on a joint work with Yaozhong Hu and David Nualart.

** Wednesday, November 16th**

COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: Stabilized numerical methods for fluid-structure interactions with application in vascular blood flow simulations

SPEAKER: Yue Yu, Lehigh University

TIME: 3:35pm – 4:35pm

ROOM: Ayres 113

In this work, we consider the partitioned approach for fluid-structure interactions, and we develop new stabilized algorithms. There are two approaches in formulating the discrete systems in simulating fluid-structure interaction (FSI) problems: the monolithic approach, and the partitioned approach. The former is efficient for small problems but does not scale up to realistic sizes, whereas the latter suffers from numerical stability issues. In particular, in vascular blood flow simulations where the mass ratio between the structure and the fluid is relatively small, the partitioned approach gives rise to the so-called added-mass effect which renders the simulation unstable. I will present a new numerical method to handle this added-mass effect, by relaxing the exact no-slip boundary condition and introducing proper penalty terms on the fluid-structure interface, which enables the possibility of stable explicit coupling procedure. The optimal parameters are obtained via theoretical analysis, and we numerically verify that stability can be achieved irrespective of the fluid-structure mass ratio. To demonstrate the effectiveness of the proposed techniques in practical computations, I will also discuss two vascular blood flow applications in three-dimensional large scale simulations. The first application is obtained for patient-specific cerebral aneurysms. The 3D fractional-order PDEs (FPDEs) are investigated which better describe the viscoelastic behavior of cerebral arterial walls. In the second application, we apply the stabilized FSI method to heart valves, and simulate the coupling of the bioprosthetic heart valve and the surrounding blood flow under physiological conditions.

** Thursday, November 17th **

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: A system of Korteweg-de Vries type equations with coupled quadratic nonlinearities: global well-posedness and stability of solitary wave solutions

SPEAKER: Michael Morgan Wise, UTK

TIME: 2:00pm – 3:00pm

ROOM: Ayres 112

In this discussion, systems

u_t+u_xxx+P(u,v)_x=0

v_t+v_xxx+Q(u,v)_x=0

of Korteweg-de Vries (KdV) type are considered. The nonlinearities P and Q are homogeneous, quadratic polynomials in u and v with real coefficients. A condition on P and Q sufficient for global well-posedness of the initial-value problem with initial data in H^s (R)×H^s (R) for s>-3/4 will be discussed. Attention will be drawn to solitary-wave solutions of the system above and special traveling waves called proportional solitary waves will be introduced. Under the same conditions provided for global well-posedness of the initial value problem, criteria for stability of these traveling-wave solutions will be given. This talk is a summary of a paper by Bona, Cohen, and Wang (2013) and another by Bona, Chen, and Karakashian (2015).

JR. COLLOQUIUM

TITLE: Where Can Graduate Study in Mathematics Take Me?

SPEAKER: Peter Perry, University of Kentucky

TIME: 3:40pm-4:30pm

ROOM: Ayres 405

Graduate study in mathematics can open up many different career possibilities in teaching, industry, and government. In this talk we'll look at some career trajectories of graduate students, how graduate school connected these students with opportunities, and how you can apply to graduate programs, evaluate offers, and make a sound decision. After a thirty-minute presentation I'll open up the floor for questions and discussion.

Note: Perry was Director of Graduate Studies at the University of Kentucky from 2012 to 2016 and directs the Graduate Scholars in Mathematics program at the University of Kentucky.

**Friday, November 18th **

COLLOQUIUM

TITLE: Homogenization of Stochastic and Heterogenous Models in Porous Media

SPEAKER: Hakima Bessaih, University of Wyoming

TIME: 3:40pm-4:30pm

ROOM: Ayres 405

We study Brinkman's equations with microscale properties that are highly heterogeneous in space and time. The time variations are controlled by a stochastic particle dynamics described by a stochastic differential equation (SDE). Our main results include the derivation of macroscale equations and showing that the macroscale equations are deterministic.

We use the asymptotic properties of the SDE and the periodicity of the Brinkman’s coefficient in the space variable to prove the convergence result. The SDE has a unique invariant measure that is ergodic and strongly mixing. The macro scale equations are derived through an averaging principle of the slow motion (fluid velocity) with respect to the fast motion (particle dynamics) and also by averaging the Brinkman's coefficient with respect to the space variable. Our results can be extended to more general nonlinear diffusion equations with heterogeneous coefficients.

This is a joint work with Yalchin Efendiev and Florian Maris.

*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:**