Seminar Schedule
April 25-29, 2005
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
Algebra
Joint meeting with VIGRE-Algebra, please see Wednesday, April 27, 2005
Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea
Topology
3:30-4:30p.m., Room 326
Speaker: Ken Baker, University of Georgia
Title of talk: Ozsvath-Szabo Invariants (cont.)
VIGRE Graduate Student Seminar
2:00p.m., Room 304
No meeting this week
Dynamics on Berkovich Spaces
2:30 PM Room 326
No meeting this week
Spline Analysis
1:30-2:30pm, Room 326
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: 3D Steady State Navier-Stokes Equations
Abstract: I will explain basic theory of 3D Navier-Stokes equations,
weak formulation,
existence and uniqueness.
VIGRE – Cardiac Physiology
2:30p.m., Room 640
Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea
Algebraic Geometry
2:30p.m., Room 410
Speaker: Joe Rusinko, University of Georgia
Title of talk: String polytopes and Mirror Symmetry
Abstract: Given a small toric degeneration from W to X, Batyrev
gives a construction of mirror families of Calabi-Yau hypersurfaces in W, for
CY-hypersurfaces in X. We will discuss an attept to show that the toric degenerations
of Alexeev and Brion, of the flag variety G/B to toric varieties given by string
polytopes, is in fact a small toric degeneration.
We will see how this leads to a study of the vertices of the string polytopes. We also will discuss the possibility of describing the string polytopes as the Minkowski sum of the polytopes you get by degenerating grassmanians inside of G/B.
VIGRE-Algebra – joint meeting with Algebra
3:30-4:30pm, Room 303
Speaker: Jon Kujawa, University of Georgia
Title of talk: Lie theory for the symmetric groups, continued.
Abstract: We will continue our discussion of the Lie theoretic
approach to the symmetric groups. In particular, we will be sure to say the
phrase "Gelfand-Zetlin" at some point during the talk.
Number Theory
3:45-5:15pm, Room 304
No meeting this week
VIGRE – Algebraic Geometry
2:00p.m., Room 304
Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea
Colloquium
3:30p.m., Room 304
Speaker: M.W. Wong, York University, Toronto, Canada
Title of talk: Weyl Transforms, the Heat Kernel and Green
Function of a Degenerate Elliptic Operator
Abstract: We give a formula for the heat kernel of a degenerate
elliptic partial differential operator $L$ on $BbbR^2$ related to the Heisenberg
group. The formula is derived by means of pseudo-differential operators of the
Weyl type, I.e., Weyl transforms, and the Fourier-Wigner transforms of Hermite
functions. Using the heat kernel, we give a formula for the Green function of
$L$. Applications to the global hypoellipticity of $L$ in the sense of Schwartz
distributions and the ultracontractivity of the strongly continuous one-parameter
semigroup $e^{-tL}, t > 0$, are given.
Geometry
2:30p.m., Room 326
Speaker: TBA
Title of talk: TBA
VIGRE – Clifford Algebras
3:30-4:45p.m. Room 302
Joint Analysis
3:30p.m., Room 303
Speaker: Gerd Mockenhoupt, Georgia Tech
Title of talk: On restrictions of the Fourier Transform
Wavelet Analysis
3:30-4:30p.m., Room 322
Speaker: Alla Balueva, University of Georgia
Title of talk: A New Numerical-Analytical Method for Solution
of 3D Mixed Boundary Value Problems
Abstract: Integro-differential equations will be constructed
to model how cracks expand. The problems about cracks occupying some domain
in the plane in 3-dimensional elastic medium may be viewed as the mixed boundary-value
problems for the displacements of the elastic medium: Laplaces equation of three
variables + the derivative of the displacements given in the domain of the crack
and the displacements given = 0 outside the domain. The solution to this mixed
Dirichlet/Neumanns problem possesses the singularity on the boundary of the
domain, so the use of the Finite Element Methods for the solution is not applicable.
Besides, we need the solution not for a whole 3D space, but only in the domain
of the crack (we are interested only in the crack aperture and are not interested
in the other displacements of the body around).
The 3D boundary-value problem will be reduced to an integro-differential equation
in the crack domain using the Green function theory. For the calculation of
the boundary elements first the analytical procedure is used. The method will
use Fourier transforms and the property of convolution of the functions under
the integral. Due to the fact that the linear splines chosen have the Fourier
transform in closed form, and the latter are oscillating, it turns out that
its possible to derive the asymptotic formula for calculation of the boundary
elements. During the numerical calculations, only a few first elements are calculated
by integration, but all the rest are calculated by an analytical formula. Obviously,
this would reduce the time of calculation by thousand times compared to the
time spent in finite or boundary element methods, and our 3D package runs just
for several minutes. At the end the 3D software package will be demonstrated
to show how cracks expand.