Seminars and Colloquiums
for week of October 10, 2011
Speaker:
Ms. Ellie Abernethy, Monday
Mr. Joseph White, Wednesday
Dr. Luis Finotti, Thursday
Sharon Bewick, Thursday
Dr. Luan Hoang, Dept. of Mathematics & Statistics, Texas Tech University, Lubbock TX, Friday
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, October 10, 2011
Algebra Seminar
TIME: 2:30 – 3:20
ROOM: Ayres Hall B004
SPEAKER: Ms. Ellie Abernethy
TITLE: K_0(R)
Wednesday, October 12, 2011
Analysis Seminar
TIME: 3:35 – 4:25
ROOM: Ayres 113
SPEAKER: Mr. Joseph White
TITLE: Hadamard matrices and Subfactors
ABSTRACT : A (complex) Hadamard matrix is a square orthogonal matrix having all entries of absolute value 1. In this introductory talk, we will present what is known about complex Hadamard matrices and how they connect to subfactors, via commuting squares and Jones' basic construction.
Thursday, October 13, 2011
Sage Workshop
TIME: 10:00 – 10:50
ROOM: Ayres 114
SPEAKER: Dr. Luis Finotti
TITLE: Introduction to Sage
ABSTRACT : Sage is a free (as in "freedom" and as in "no cost") and powerful mathematics software that aims to compete with commercial products such as Maple, Mathematica, MATLAB, and MAGMA. In many areas it is in fact superior to those.
After an initial discussion about the organization of the workshop, I will talk about the basics of Sage, such as brief history, strong and weak points, installation, documentation and help, range of possible applications, syntax, and basic examples, such as symbolic computation, graphing, calculus and linear algebra examples.
(Depending on time, some of these might be left to the following meeting.)
Math Biology Seminar
TIME: 12:45 – 1:35
ROOM: NIMBioS Classroom
SPEAKER: Sharon Bewick
TITLE: Dynamics of Animal Grouping
Friday, October 14, 2011
Colloquium
TIME: 3:35 – 5:00pm
ROOM: Ayres 405
SPEAKER: Dr. Luan Hoang, Dept. of Mathematics & Statistics, Texas Tech University, Lubbock TX
TITLE: Navier--Stokes equations and Geophysical Fluid Dynamics
ABSTRACTNavier--Stokes equations are a system of nonlinear partial differential equations describing the dynamics of incompressible fluids. Despite its importance in fluid mechanics, the basic question of the existence of regular solutions for all time is still open. Therefore it is crucial to obtain the global well-posedness in certain contexts, particularly for practical applications.
We first survey the global well-posedness for some models in geophysical fluid dynamics. Two approaches are pointed out: simplifying the Navier--Stokes equations under consideration of the size of physical parameters (e.g.~primitive equations) or studying Navier-Stokes equations directly with extreme values of those parameters (e.g.~thin domains or fast rotation). This talk will focus on the second approach, particularly for thin domains.
The first results on the global well-posedness for Navier--Stokes equations in a thin domain were obtained by Genevieve and Sell in 1993. Since then there have been a large number of similar results established mostly for Dirichlet, Neumann, periodicity boundary conditions and mainly for flat boundaries. Only few are for free boundary conditions or strictly spherical domains. There are a couple of papers on two-layer fluids with interface boundary conditions.
Here we study two-layer incompressible fluids in a thin domain whose top, bottom and interface boundaries are not flat. The fluid is subject to the Navier friction boundary condition on the top and bottom, and the periodicity condition on the sides. On the interface boundary, similar conditions on the normal stress of both fluids relating to their relative velocity are imposed. This is considered as a toy model for the coupled atmosphere and ocean problem.
We prove that regular solutions exist for all time when the initial data and body force are large, though not arbitrarily, as the thickness of the domain becomes small. To deal with the involved boundary conditions on surfaces of non-trivial geometry, appropriate boundary behaviors of the fluid are derived and used in obtaining good estimates for the Stokes operator and for the nonlinear terms of Navier--Stokes equations. Our approach gives a unified treatment for both the Navier and interface boundary conditions.
Past notices:
Seminars from 2010-2011 academic year
Seminars from 2009-2010 academic year
Seminars from 2008-2009 academic year
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year