Seminars and Colloquiums
for the week of April 6, 2009
Speakers:
Mr. Mike Kelly, Monday
Professor Tai-Chia Lin, National Taiwan University, Tuesday
Dr. Andreas Basse, Department of Mathematical Sciences, Aarhus University, Denmark , Thursday
Monday, April 6
MATH ECOLOGY SEMINAR
TIME: 11:15 – 12:05
ROOM: Dabney 575
SPEAKER: Mike Kelly
TITLE: “Harvesting in Fishery Models”
Tuesday, April 7
DE & COMPUTATIONAL APPLIED MATH SEMINAR
TIME: 3:35 – 4:35
ROOM: HBB 102
SPEAKER: Professor Tai-Chia Lin, National Taiwan University
TITLE: “Self-similar solutions of two-component system of nonlinear Schrodinger equations”
ABSTRACT: Conventionally, to learn wave collapse and optical turbulence, one must study finite-time blow-up solutions of one-component self-focusing nonlinear Schrodinger equations (NLSE). Here we consider simultaneous blow-up solutions of two-component systems of self-focusing NLSE. By studying the associated self-similar solutions, we prove two components of solutions blow up at the same time. These self-similar solutions may
have k-fold Townes and ring profiles forming abundant geometric patterns which cannot be found in one-component self-focusing NLSE. Numerical results provide another self-similar solutions with multiple ring and Townes profiles which have not yet been proved rigorously. These results may provide the first step to investigate optical turbulence in two-component systems of NLSE.
Thursday, April 9
PROBABILITY SEMINAR
TIME: 12:40 p.m.
ROOM: HBB 132
SPEAKER: Dr. Andreas Basse, Department of Mathematical Sciences, Aarhus University, Denmark
TITLE: "Moving Averages and Semimartingales."
ABSTRACT: Continuous time moving averages X, as e.g. the fractional Brownian motion, the Ornstein-Uhlenbeck process and their generalizations, have been used repeatedly in finance, turbulence and related fields. In general it is important to known when a process is a semimartingale; in this respect the Bichteler-Dellacherie characterization of semimartingales as stochastic integrators is crucial. The aim of this talk is to study when a moving average is a semimartingale; various filtrations are considered. We will focus on following two cases, when the driving process Z is a Levy process and the filtration is generated Z, and when the driving process is a Brownian motion and the filtration is generated by X. Some path properties of X will be discussed as well. Examples including fractional Levy processes and in particular the linear fractional stable motion will be considered. If time allows we will also discuss the semimartingale property of moving averages in a chaos setting. This part is based on a new integrability result for seminorms.
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:
3/16/09 (spring break)
Past notices:
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year