**Seminars and Colloquiums**

for the week of March 19, 2018

for the week of March 19, 2018

*SPEAKERS*

**Tuesday**

Vy Nguyen, University of Tennessee

**Wednesday**

Adam Spannaus and Jonathan Hicks, University of Tennessee

**Thursday**

Ibrahim Aslan and Mahir Demir, University of Tennessee

Richard Rebarber, University of Nebraska – Lincoln

Claudia Rawn, University of Tennessee

Kyeongsu Choi, MIT

**Friday**

Martin Reiris, Universidad de la República, Uruguay

*TEA TIME
3:00 PM – 3:30 PM
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted by: Cara Sulyok and Shuler Hopkins*

**Tuesday, 3/20**

STOCHASTICS/PROBABILITY SEMINAR

TITLE: The description of Levy measures of Squared Bessel Processes

SPEAKER: Vy Nguyen, University of Tennessee

TIME: 2:10 PM-3:20 PM

ROOM: Ayres 114

If B is a Brownian motion in Rd (the position of a particle moving in space at random), then the distance of B to the origin is a Markov process called a d-dimensional Bessel process. Bessel processes are recognized as one of the most important one dimensional diffusions. They are a part of Markov processes theory and stochastic analysis. The most recent applications of Bessel (and squared Bessel) processes include financial mathematics. Squared Bessel processes contain the same amount of information as Bessel processes (they are also Markov) but are used more often in stochastic calculus. The squared Bessel processes are infinitely divisible by a result of Shiga and Watanabe. In this talk, I will present the description of Levy measures of Squared Bessel Processes using the Ray-Knight theorem and the excursion theory of Brownian motion

**Wednesday, 3/21**

COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: Annealed Importance Sampling

SPEAKER: Adam Spannaus, University of Tennessee

TIME: 3:35 PM-4:35 PM

ROOM: Ayres 112

The process of Simulated Annealing-moving from a distribution that is readily sampled from to one where samples are not easily drawn by a sequence of intermediate distributions-was introduced by Metropolis in 1953 and described in an optimization context by Kirkpatrick in 1983.

In both cases, samples are obtained by Markov Chain Monte Carlo techniques, and might fail to accurately represent an isolated mode. In this talk, we present the Annealed importance sampler of Neal. We will show how one can move from a tractable distribution to a target distribution by a sequence of intermediate distributions. Incorporating Markov chain transitions into the importance sampling method allows for the method to efficiently sample from high-dimensional distributions and those with isolated modes. We will show how normalizing constants can be readily computed and illustrate the theory through numerical examples.

TITLE: Saddle Points on Potential Energy Surfaces

SPEAKER: Jonathan Hicks, University of Tennessee

TIME: 3:35 PM-4:35 PM

ROOM: Ayres 112

We will begin with a discussion of Potential Energy Surfaces (PES) by giving an overview of what a PES is with some of its properties, namely Index-1 Saddle Points. A common Potential Energy Function known as the Lennard-Jones Pair Potential is reviewed and some relaxed state particle configurations are shown. We will then investigate finding saddle points by use of The Dimer Method. The Dimer Method consists of two parts involving a rotation and translation. Each of these will be discussed as it pertains to finding saddles points on PES.

**Thursday, 3/22**

MATH BIOLOGY SEMINAR

TITLE: Optimal monitoring and control under state uncertainty: Application to lionfish management

SPEAKER: Ibrahim Aslan and Mahir Demir, University of Tennessee

TIME: 11:10 AM-12:00 PM

ROOM: Hesler 427

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: A length-structured density dependent model for fish.

SPEAKER: Richard Rebarber, University of Nebraska – Lincoln

TIME: 2:10 PM-3:10 PM

ROOM: Ayres 114

We propose a length-structured model for fish, where the probability of a fish growing to a larger length class is nonlinearly decreasing with the population biomass. Our model is a discrete-time matrix model with nonlinear stage-transitions. We analyze this model mathematically, connecting persistence, boundedness, blow-up and equilibria to spectral radii of easily computed matrices. We illustrate this theoretically and numerical with White Perch, a species that is invasive in Nebraska. For this species the model predicts (and the data shows) that the small fish crowd out the large fish.

JR. COLLOQUIUM

TITLE: Math and Materials Science and Engineering

SPEAKER: Claudia Rawn, University of Tennessee

TIME: 3:40 PM-4:35 PM

ROOM: Ayres 405

Materials Science and Engineering (MSE) is meeting ground for Biology (biomaterials), Chemistry, Mathematics, and Physics. MSE students at the University of Tennessee, Knoxville take Calculus I, II, III, Matrix Computations, and Differential Equations I. The foundation of MSE is structure-processing-properties where structure can be on various scales including the atomic scale or on the order of 10-10 m or an Å. X-ray diffraction is a tool used for probing the atomic structure. Like each person has a unique fingerprint each compound with its unique atomic arrangement and chemistry has a unique diffraction pattern. We can calculate the position of the diffraction peaks by knowing the dimensions of the smallest repeating building block and the intensity of the peaks by the atom species and locations. Which peaks are absent depend on the symmetry of the atomic arrangement. In this seminar we will talk about the history of X-ray and neutron diffraction and go over some of the equations we use for the calculations above.

GEOMETRIC ANALYSIS SEMINAR

TITLE: Free boundary problems in the Gauss curvature flow

SPEAKER: Kyeongsu Choi, MIT

TIME: 5:05 PM-6:05 PM

ROOM: Ayres 113

We will discuss the optimal $C^{1,1/(n-1)}$ regularity of the Gauss curvature flow with a flat side. We will consider several quantities which are degenerate or singular near the flat side, and establish estimates for their ratios. The geometric meaning of the ratios will be discussed. Moreover, using these ratios, we will classify the closed self-similar solutions to the Gauss curvature flow.

**Friday, 3/23**

COLLOQUIUM

TITLE: Bakry-Émery geometric comparison techniques and applications to general relativity

SPEAKER: Martin Reiris, Universidad de la República, Uruguay

TIME: 3:35 PM-4:35 PM

ROOM: Ayres 405

Starting with the work of Bakry, Émery, Ledoux, and others on diffusion processes on Riemannian manifolds, several novel Riemannian-comparison techniques with broad applications have been developed over the last decades. Classical theorems, like Myer's compactness or Cheeger-Gromoll's splitting were generalised and impressive applications were found by Perelman in the Ricci flow and soliton's theory. In this talk I will begin reviewing the probabilistic origins of such techniques, introduce then some basic theorems, and finally show applications to a wide range of problems related to static and stationary solutions of the Einstein equations (the 'solitons' of the theory) with or without matter. Open problems and prospective directions of work will be mentioned.

*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:**

3_12_18 (spring break)