Seminars and Colloquiums
for the week of January 19, 2009
Speakers:
Professor B. G. Kang, POSTECH, Korea, Wednesday
Professor Stefan Richter, Wednesday
Mr. Brendon LaBuz, Wednesday
Professor Michael Frazier, Thursday
Mr. Shiying Si, Thursday
Dr. Debra Warne, James Madison University, Friday
Wednesday, January 21
ALGEBRA SEMINAR
TIME: 3:20 p.m.
ROOM: HBB 102
SPEAKER: Professor B. G. Kang, POSTECH, Korea
TITLE: “Recent Progress on Pi-Domains”
ABSTRACT: We prove that the full power-series ring over a regular ring is a Pi-Domain.
ANALYSIS SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: HBB 112
SPEAKER: Professor Stefan Richter
TITLE: “Extensions and dilations of operator tuples”
TOPOLOGY SEMINAR - postponed
TIME: 3:35 – 4:25 p.m.
ROOM: AC 113
SPEAKER: Brendon LaBuz
TITLE: Uniform (local) joinability vs. coverability
ABSTRACT: Professor Plaut published the paper "An Equivalent Condition for a Uniform Space to be Coverable" devoted
to proving that the class of chain connected coverable spaces (defined by Berestovskii and Plaut) is the same as the class of chain
connected uniformly (locally) joinable spaces (defined by Brodskiy, Dydak, LaBuz, and Mitra). I will construct a space as a counterexample to proofs of two propositions in the paper as well as point out the flaw in another proof.
Thursday, January 22
PROBABILITY SEMINAR
TIME: 12:40 p.m.
ROOM: HBB 132
SPEAKER: Mr. Shiying Si
TITLE: "Two-step variation for processes driven by fractional Brownian motion with applications in testing for jumps in the high frequency data. Part 1."
ABSTRACT: The theory of bipower variation has developed from problems of detecting and modeling jumps in the financial data. We introduce the two-step variation, which is similar but different from the bipower variation. We develop limit laws for the two-step variation of the integral with respect to fractional Brownian motion, and more generally, with respect to Gaussian processes with stationary increments. As application we obtain a statistical test for detecting jumps in the high frequency data. Our methods include tools from ergodic theory and Malliavin calculus.
JUNIOR COLLOQUIUM
TIME: 3:40 p.m.
ROOM: AC 113A
SPEAKER: Professor Michael Frazier
TITLE: “Applications of Wavelets: Fingerprints, Submarines, and Car Rattles”
ABSTRACT: One of the remarkable things about mathematics is how an idea developed in one context can have applications far outside the scope of its origination. Early in my career as a pure
mathematician, I collaborated in some work that was a precursor to the theory of "wavelets."
Wavelets are functions that look like small waves; they are localized in space but they oscillate
like a sine or cosine function. It turns out that all reasonable functions can be constructed as a superposition of wavelets. I will discuss some applications of wavelets, including the computerization of the FBI fingerprint files, and two projects that I contributed to: One to track enemy submarines in the ocean, and one to automate the diagnosis of car problems based on the sound the car makes.
Friday, January 23
COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: AC 113A
SPEAKER: Debra Warne, James Madison University
TITLE: “A 3D Nonlinear Anisotropic Spherical Inflation Model for Intracranial Saccular Aneurysm Elastodynamics”
ABSTRACT: Intracranial arterial (or cerebral) aneurysms occur in weakened areas of artery walls
resulting in a ballooning out of the wall filled with blood. A major catalyst for mathematical
modeling of intracranial saccular aneurysms has been the axisymmetric membrane derivations in Shah and Humphrey (1999, Journal of Biomechanics, 32, 593—599) and David and Humphrey (2003, Journal of Biomechanics, 36, 1143—1150). We expand on the foundational membrane dynamics to develop a blood-aneurysm-cerebrospinal fluid model from the fully three-dimensional nonlinear elastic equations of motion with system coupling at both inner and outer fluid-aneurysm boundaries consistent with Navier-Stokes. The motion is driven by tractions at the inner and outer boundaries resulting from the biological forcing of the blood (interior to the aneurysm) and the cerebrospinal fluid (exterior to the aneurysm). We derive the 3D elastodynamics and determine subsequent governing nonlinear ordinary differential equations for the three general material symmetries possible under the classic initial assumption of axisymmetry. We employ biologically motivated strain-energy functions, including limiting chain extensibility arterial tissue constitutive models, to numerically solve the equations and observe resulting aneurysm cyclic stretches, thickness changes, effects of material and geometric parameters, and through-the thickness stresses due to biological forcing for each type of material symmetry and constitutive model. As hemodynamic factors and forces due to blood pressure are important considerations in aneurysm dynamics, mathematical models of the sort developed here are useful for numerous modeling scenarios, especially in light of limited experimental data and difficulties associated with in vivo observations. While aneurysm rupture is widely believed to occur when hemodynamically induced wall stress exceeds wall strength, there have been few rigorous biomechanical analyses. Models characterizing intra-aneurysmal stresses should be useful in developing insights and simulations toward a better understanding of when a catastrophic event may occur.
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. Steve Wise.
Week of:
Past notices:
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year