For
Monday, April 4, 2005
the Week's Events
finger seminar@math.utexas.edu or see http://www.ma.utexas.edu/cgi-pub/seminar/calendar
2:00 pm Monday, April 4, 2005
Topology Seminar
:
Exotic smooth structures on rational surfaces
by
Andras Stipsicz
(The Renyi Institute, Budapest, and IAS Princeton) in RLM 11.176
Most known smoothable simply connected 4--manifolds admit infinitely many different smooth structures (distinguished, for example, by Seiberg--Witten invariants). There are some 4--manifolds, though, for which the existence of such 'exotic' structures is still open, the most notable examples being the 4--dimensional sphere S^4 and the complex projective plane CP^2. In a recent project with Z. Szabo and J. Park we found constructions of exotic smooth structures on the five- and six-fold blow--up of CP^2. In the lecture we describe the construction of these 4--manifolds and indicate the necessary input from Seiberg--Witten theory for proving their exoticness.
3:00 pm Monday, April 4, 2005
Junior PDE Seminar
:
A brief introduction to the Bellman equation.
by
Russell Schwab
(UT Austin) in RLM 10.176
The Bellman equation is a famous and useful type of nonlinear first order PDE. We will show where it comes from in optimal control theory and discuss some of its properties.
4:00 pm Monday, April 4, 2005
Jr. Algebra
:
Generic Galois extensions and rigidity
by
Kelly McKinnie
(U.T. Austin) in 12.166
9:30 am Tuesday, April 5, 2005
Introduction to Mathematical Research at UT-Austin
: by
Daniel Allcock
in RLM 10.176
12:30 pm Tuesday, April 5, 2005
GADGET
:
The Yamabe problem and some fully nonlinear generalizations
by
Maria del Mar Gonzalez
(UT Austin) in RLM 9.166
This is the first of two talks in conformal geometry. We will explain first the classical Yamabe problem (construct a constant scalar curvature metric in the same conformal class as a given metric), for a compact manifold without boundary. Then we will consider the same problem on a complete, non-compact manifold. PDE's play an important role in both, however, the talk will be Geometry oriented.
2:00 pm Tuesday, April 5, 2005
Number Theory Seminar
:
Elliptic Divisibility Sequences
by
J. Silverman
(Brown) in RLM 9.166
An *Elliptic Divisibility Sequence* is a sequence of integers
described by the nonlinear recursion
This is the same recurrence that is satisfied by the division polynomials of an elliptic curve, so (almost) equivalently one can attach an elliptic divisibility sequence to a point of infinite order
on an elliptic curve by writing
and setting
. In this talk I will discuss various properties of elliptic divisibility sequences, including their sign variation over
(joint work with N. Stephens), convergence properties of subsequences in
, conjectural gcd growth bounds over
, and if time permits, results over function fields.
11:00 am Wednesday, April 6, 2005
Mathematical Physics Seminar
:
To Be Announced
by
Robert McCann
(University of Toronto) in RLM 12.166
11:00 am Wednesday, April 6, 2005
Mathematical Physics Seminar
:
Exact semi-geostrophic flows in an elliptical ocean basin
by
Robert McCann
(University of Toronto) in RLM 12.166
A new family of exact solutions is analyzed, which model 2D circulations of an ideal fluid in a uniformly rotating elliptical tank, under the semi-geostrophic approximation from meteorology and oceanography. The fluid pressure and stream function remain quadratic functions of space at each instant in time, whose fluctuations are described by a single degree of freedom Hamiltonian system depending on two conserved parameters: domain eccentricity and the constant value of potential vorticity. These parameters determine the presence or absence of periodic orbits with arbitrarily long periods, fixed points of the dynamics, and aperiodic homoclinic orbits linking hyperbolic saddle points. The energy relative to these parameters selects the frequency and direction in which isobars nutate or precess, as well as the steady circulation direction of the fluctuating flow. The canonically conjugate variables are the moment of inertia and angle of inclination of an elliptical inverse-potential-vorticity patch evolving in dual coordinates.
1:00 pm Wednesday, April 6, 2005
Analysis seminar
:
Geometric properties in Parabolic Flows and Nonlinear Elliptic Eiegenvalue problems
by
Ki-ahm Lee
(UT Austin) in RLM 10.176
2:00 pm Wednesday, April 6, 2005
Junior Topology Seminar
:
Disks in the Heisenberg Group
by
Eric Katerman
in RLM 11.176
An automatic group is a group whose Cayley graph you can "see". We will formalize this notion, give examples and non-examples of automatic groups, and prove that the three-dimensional integral Heisenberg group is not automatic by considering disks in its Cayley graph. The argument will involve one "proof by machines" and at least two proofs by pictures.
You are invited to view the teaser trailer here:
http://math.utexas.edu/~katerman/topology.mov
4:00 pm Wednesday, April 6, 2005
Working Dynamical Systems
:
Lorenz Template
by
Bob Williams
in RLM 10.176
Bob is going to tell us a bit about the Lorenz Template.
9:30 am Thursday, April 7, 2005
Introduction to Mathematical Research at UT-Austin
: by
Lauren Meyers
(Integrative Biology) in RLM 10.176
2:00 pm Thursday, April 7, 2005
Number Theory Seminar
:
To Be Announced
by
R. Conceicao
(UT) in 9.166
candidacy talk
3:30 pm Thursday, April 7, 2005
Geometry Seminar
:
To Be Announced
by
Samuel Grushevsky
(Princeton) in RLM 9.166
12:00 pm Friday, April 8, 2005
Sophex
:
TBA
by
Renato Calleja
in RLM 9.166
TBA
1:00 pm Friday, April 8, 2005
Financial Mathematics
:
To Be Announced
by
Simon Brendle
(Princeton) in RLM 11.176
http://www.ma.utexas.edu/Seminars/MathFin/
1:00 pm Friday, April 8, 2005
Analysis seminar
:
Some computational methods for the solution of fully nonlinear elliptic equations of the Monge-Ampere type
by
Roland Glowinski
(University of Houston) in RLM 10.176
3:00 pm Friday, April 8, 2005
Junior Geometry
:
Mirror Symmetry Musings
by
Phillip Schmitz
(UT Austin) in RLM 9.166
A whirlwind tour of the mathematics aspects of Mirror Symmetry based mainly on Morrison's survey (alg-geom/9609021). In a vain attempt at being self-contained it is sure to include vague references to correlation functions, pseudoholomorphic curves, Gromov-Witten invariants and moduli spaces. Actual calculations may also be featured.