Un of Tenn | Math Department

Seminars and Colloquiums
for the week of April 2, 2012

Speaker:

Mr. Jason Bintz & Mr. Mike Kelly, Monday
Mr. Zhiqiang Li, Monday
Ms. Beth Lewis, Monday
Ms. Ashley Rand, Wednesday
Dr. Stephen Shipman, LSU, Wednesday
Professor Mishko Mitkovski, Georgia Tech, Wednesday
Mr. James Ashe, Thursday
Ms. Anastasiia Tsvietkova, Thursday
Prof. Stephen Shipman, LSU, Thursday

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 Dr. Judy Day.

Monday, April 2

MATH BIOLOGY SEMINAR
TIME: 2:30 - 3:20 p.m.
ROOM: Ayres 121
SPEAKER: Mr. Jason Bintz & Mr. Mike Kelly
TITLE: Introduction of Agent-based Models (part 2)

PROBABILITY SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 122
SPEAKER: Mr. Zhiqiang Li
TITLE: Stability of filter with Poisson observations
ABSTRACT: The short interest rate process is modeled by an asymptotically stationary diffusion process. With the counting process observations, a filtering problem is formulated and its exponential stability is derived.

ALGEBRA SEMINAR
TIME: 3:35 - 4:25 p.m.
ROOM: Ayres B004
SPEAKER: Ms. Beth Lewis
TITLE: The zero-divisor graph of a commutative semigroup
ABSTRACT: Let S be a commutative semigroup with 0. The zero-divisor graph of S is the simple graph with vertices the nonzero zero-divisors of S and two distinct vertices x and y are adjacent if xy = 0. We will discuss some properties of this graph.

Wednesday, April 4

TOPOLOGY SEMINAR
TIME: 2:30 - 3:20 p.m.
ROOM: Ayres Hall G004
SPEAKER: Ms. Ashley Rand
TITLE: The Zariski Topology
ABSTRACT: Let R be a commutative ring with spec(R) its set of prime ideals. We discuss a topology on spec(R) called the Zariski topology and some of the basic properties.

JUNIOR COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 405
SPEAKER: Dr. Stephen Shipman, LSU
TITLE: Simple models for complex physical phenomena
ABSTRACT: Real physical systems are usually too complicated to describe mathematically in detail. What we try to do instead is to isolate essential features of a system and devise an analytically tractable model system that exhibits those features. I will illustrate this philosophy with a simple chain of beads connected by springs that nicely exhibits the phenomena of wave propagation and inhibition in crystalline materials as well as confinement of energy at defects.

Pizza will be available at 3:15 p.m.

ANALYSIS SEMINAR
TIME: 3:35 p.m.
ROOM: Ayres 113
SPEAKER: Professor Mishko Mitkovski, Georgia Tech
TITLE: Determinacy for measures
ABSTRACT: A finite positive measure $\mu$ is said to be $a$-determinate if there is no other finite positive measure $\nu$ such that the Fourier transforms of $\mu$ and $\nu$ agree on some interval of length $a$. For a given measure $\mu$ we show how to compute the largest $a$ for which $\mu$ is $a$-determinate by looking only at the support of $\mu$. Our approach is based on the de Branges-Naimark extreme point method. We use the same method to give a very short proof of the result of Eremenko and Novikov concerning oscillations of measures with a spectral gap. This is joint work with A. Poltoratski.

Thursday, April 5

DOCTORAL DEFENSE
TIME: 10:00 a.m.
ROOM: Ayres 122
SPEAKER: Mr. James Ashe
TITLE: Generalized Branching in Circle Packing
His committee consists of Professors: Stephenson (chair), Brodskiy, Collins, and Hinde (Chemistry).

DOCTORAL DEFENSE
TIME: 2:10 p.m.
ROOM: Ayres 114
SPEAKER: Ms. Anastasiia Tsvietkova
TITLE: Hyperbolic structures from link diagrams
Her committee consists of Professors: Thistlethwaite (chair), Conant, Plaut, and Berry (EECS).

COLLOQUIUM
TIME: 3:35 – 4:25 pm
ROOM: Ayres 405
SPEAKER: Prof. Stephen Shipman, LSU
TITLE: Resonance of Fano Type in Photonic Structures
ABSTRACT: This presentation will begin with a review of various mechanisms of resonance in photonic systems, including those known as "Fabry-Perot resonance", "Wood anomalies", and scattering resonances. Then it will focus on the latter. We consider photonic structures that are in contact with an ambient space, such as an open periodic waveguide or a localized defect within a closed waveguide. Under special conditions, an open structure can admit a monochromatic bound state, exponentially confined to the structure. Such a state is typically unstable, and a general perturbation of the system couples the state to the continuum, which results in a scattering resonance. These resonances are associated with sharp anomalies in the transmissivity of incident fields and in the field amplitude within the structure. They are akin to the Fano resonance for the noble gases in quantum mechanics, in which a system with an embedded eigenvalue is perturbed. Analysis of scattering resonances as perturbations of bound states is based on singular complex perturbation analysis of the scattering problem near parameters for which the scattering problem does not admit a unique solution. The analysis applies to very general systems, discrete and continuous, and reveals fine details of the resonances, including a description of the width and center of Fano-like spikes, multiple anomalies emanating from a single frequency, and conditions that guarantee complete opacity and complete transparency at nearby frequencies. Joint work with Stephanos Venakides (Duke).

Refreshments will be available in Ayres 401 at 3:15 p.m.

Past notices:

3_26_12.html

March 19, 2012 - spring break