**Seminars and Colloquiums**

for the week of October 5, 2015

for the week of October 5, 2015

*SPEAKER:*

Michael Holloway, UTK, Monday

Logan Higginbotham, UTK, Monday

Khoa Dinh, UTK, Tuesday

Abner Salgado, UTK, Wednesday

Shijun Zheng, Georgia Southern University, Thursday

Jim Conant, UTK, Thursday

Paul J. Mlynarczyk, UTK, Friday

Ryan Loga, UTK, Friday

Chuck Collins, UTK, Friday

*Tea Time, Monday - Wednesday*

Cancelled for this week

Cancelled for this week

**Monday October 5**

GEOMETRY/TOPOLOGY SEMINAR

TITLE: Duality of Scales

TIME: 2:30 – 3:20pm

ROOM: Ayres 114

SPEAKER: Michael Holloway, UTK

Abstract: The Higson Compactification of a metric space was introduced by Higson in studying the Novikov conjecture. The Higson compactification of a proper metric space X is characterized by the property that a continuous function from X to a compact metric space extends to a continuous function on the Higson compactification if and only if that function is slowly oscillating. In this talk, the notion of a function being slowly oscillating will be extended to maps between coarse spaces and uniform spaces. This provides a means to connect the structures of the domain and codomain of the map and to study properties of both spaces. Using slowly oscillating functions, we also create a Galois connection between the set of coarse structures on the domain and the set of uniform structures on the codomain.

ALGEBRA SEMINAR

TITLE: Unimodular rows and Hermite rings III

TIME: 3:35 – 4:25pm

ROOM: Ayres 114

SPEAKER: Logan Higginbotham, UTK

Abstract: This is the third of a series of four talks whose aim is to present a proof (from a book by T. Y. Lam) of the fact that the polynomial ring in n-variables over a field, is a Hermite ring.

**Tuesday October 6**

STOCHASTICS SEMINAR

TITLE: Finding the asymptotic formula for the ground state energy of the Polaron.

TIME: 2:10 -3:25pm

ROOM: Ayres 114

SPEAKER: Khoa Dinh, UTK

ABSTRACT: In 1983 Donsker and Varadhan established a long time asymptotic result for the Polaron model in condensed matter physics. This work relied mainly on their theory in large deviation. We will draw ideas from this successful work to investigate other models.

**Wednesday October 7 **

COMPUTATIONAL & APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: Basics of Fractional ODES, Part 2

TIME: 3:35 -4:35pm

ROOM: Ayres 112

SPEAKER: Abner Salgado, UTK

Abstract: Starting from the classical tautochrone problem, I will introduce three of the basic operations in fractional calculus: the Riemann-Liouville fractional integral and derivative and the Caputo fractional derivative. We will discuss some of their most fundamental properties and the relation between them. Next, I will discuss initial value problems with Caputo fractional derivative and study the regularity of their solution and how can this regularity be used to obtain error estimates for a commonly used but not properly analyzed numerical scheme. I will conclude with some open questions.

Thursday October 8

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Sharp conditions on the global existence and blowup for rotating BEC

TIME: 2:10 – 3:25pm

ROOM: Ayres 114

SPEAKER: Shijun Zheng, Georgia Southern University

Abstract: The magnetic nonlinear Schroedinger equation (mNLS) is generated by the Hamiltonian H_{A,V}, where A represents the magnetic potential and V the electric potential. The mNLS arises in modeling dilute, trapped boson gases with rotation in ultra-cold temperature, whose mechanism in the semiclassical regime obeys the Newton’s law: x ? = ? ? ? = ??V (x) ? ? × B(x) in the transition from quantum to classical mechanics. Here B = ? ? A is the magnetic field induced by A and the Lorentz force is given by ? × B. Such systems may exhibit interesting symmetries as well as stationary wave phenomenon, accompanied by spinor and quantized vortex, a re- markable signature for the superfluidity of Bose-Einstein condensation (BEC). The earliest related result traces back to Feynman’s work on path integrals. Rigorous mathematical derivations were given by Fujiwara and Yajima. We will present recent results on the threshold for the global existence and blowup rate for the mNLS. This is joint work with Hichem Hajaiej and Yi Hu

JUNIOR COLLOQUIUM

TITLE: Tiling Problems and Modular Arithmetic

TIME: 3:40 – 4:30pm

ROOM: Ayres 405

SPEAKER: Jim Conant, UTK

ABSTRACT: Can you tile a 100x100 square grid with a 1x8 tile? It turns out that you cannot, a fact which follows from a theorem of David Klarner, published in 1969. Interestingly, the proof makes essential use of modular arithmetic. We will discuss Klarner's theorem and other related tiling problems from his 1969 paper.

**Friday October 9**

MATH BIOLOGY SEMINAR

TITLE: Designing cost-efficient surveillance for early detection and control of multiple biological invaders (from Epanchin-Niell et al. 2014 Ecological Applications paper)

TIME: 10:10 – 11:00am

ROOM: Ayres 405

SPEAKER: Paul J. Mlynarczyk, UTK

ANALYSIS SEMINAR

TITLE: An Extension Theorem for Matrix Weighted Sobolev Spaces on Lipschitz Domains part 2

TIME: 2:30- 3:20pm

ROOM: BU 476

SPEAKER: Ryan Loga, UTK

Abstract: Let D a subset R^n be a Lipschitz domain with 1 < p < infty. Suppose for each x in R^n that W(x) is an m by m positive definite matrix which satisfies the matrix A_p condition. For k=0,1,2,3,... define the matrix weighted Sobolev space L_k^p (D,W) of vector valued functions with corresponding norm. We show that for f = (f_1,..., f_m) in L_k^p(D,W) there exists an extension E(f) in L_k^p(R^n,W) such that E equals f on D and the L_k^p norm of E(f) on R^n is bounded by the L_k^p norm of f on D. This generalizes a known result for scalar A_p weights.

COLLOQUIUM

TITLE: Practical Modeling with Data

TIME: 3:35 -4:25pm

ROOM: Ayres 405

SPEAKER: Chuck Collins, UTK

Abstract: In this talk we will look at a collection of projects, each involving using modeling along with real data to find practical answers to interesting problems. The first project studies a non-linear material phenomenon, the shape-memory effect, resulting in the construction of a relevant model, computation of physically interesting results, and analysis that the model is adequate. The second project focuses on understanding and optimizing a circle packing algorithm, by modeling the problem by using a simple model for local circle relations and realizing acceleration options through large scale data analysis. The same algorithm is studied by modeling the overall process in terms of the 'flow' of geometric properties. The final and most recent project produces predictions of future occupation and estimates of the risk for the feral swine infestation in Arkansas using large sets of presence/absence and environmental data in a unique statistical model. Each of these projects involved extensive collaborations with other mathematicians and scientists

*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 *