Time and Place:
The talks will be in room 703 Thackeray Hall from 11:00AM - 12:00PM
(unless otherwise stated).
Schedule of talks
- February 12
- Speaker: Ken Chuang
- Title: Subharmonic functions on a closed Riemannian manifold
- Abstract: In this talk I will go over the proof of a theorem by E. Hopf:
every subharmonic function on a closed (i.e. compact, connected, and
boundary-free) Riemannian manifold is constant.
- March 26
- Speaker: Chris Jones
- Title: Applications of the Poisson Process
- Abstract: Death by horsekick, queues, the number of stars in a sector of
space, the number of mutations on a given strand of DNA can be modeled by
one simple probability distribution.
This subject of this talk will the applications of that distribution. The
beauty of this distribution is captured in the so-called "Strong Law of
Small Numbers."
An explanation of the current credit crisis based on this model will also
be discussed.
- March 31
- Speaker: Jonathan Holland
- Title: Audible properties of objects
- Abstract: The question of whether one can "hear the shape of a drum"
was famously posed by Mark Kac in 1966. More prosaically put, if the
Laplacians of two plane domains have the same spectrum for the
Dirichlet problem, are the domains congruent? Kac's version of the
isospectral problem, as it is known, was ultimately answered
negatively, but there is still interest in determining the invariants
of the spectrum of the Laplacian. This talk will present an
introduction to spectral invariants in differential geometry. Those of
primary importance are the heat invariants, which are local curvature
invariants, and the "determinant" of the Laplacian.
- April 9
- Speaker: Merve Kovan
- Title: Homomorphisms between Group Algebras
- Abstract: Let /G /and /H /be two locally compact abelian groups,
equipped with their Haar measures. The corresponding group algebras
are the sets of functions which are the measurable functions of whose
absolute values have finite integrals. The object of this work is to
study the structure of the Banach algebra homomorphisms between these
group algebras. The adjoint of such a homomorphism sends the dual
group of /H /into dual group of /G /union the zero function. The
problem comes to find out the mappings between the dual groups that
are induced by the adjoint of a homomorphism /h /between group
algebras.
- April 16
- Speaker: Justin Dunmyre
- Title: Topological Shooting
- Abstract: The technique referred to as "Topological Shooting" or "The
Shooting Method" is useful for analyzing ordinary differential
equations. It can be used to prove the existence of solutions to
boundary value problems, find travelling waves, or even find chaos.
Despite all these fancy words, the basic technique is very easy to
understand. I will present the core theorems needed (if you took Adv.
Calc, you know half of them!), and then show how the technique can be
used to find a periodic solution to a nonlinear, non-autonomous ODE.
Purpose:
- It is the purpose of this seminar to give graduate students
a chance to
give presenations to audiences. The topics do not have to be original
work. You may present a paper or other interesting topic. The
presentations
should accessible to the entire graduate student body.
- Another purpose is to provide graduate students with free
pizza and
(soft) drinks.
Contact:
If you'd like to give a talk, please email Nate at nhm3 (at) pitt.