Inverse problems theme year 2003-2004
Inverse Problems Seminar Week
Helsinki, Finland, 24 to 28 May 2004
Most lectures are given in seminar rooms S III and S IV
at the Department of Mathematics
and Statistics of the
University of Helsinki,
address Yliopistonkatu 5, 5th floor (S IV)
and 5th floor (S IV).
Floquet theory of periodic elliptic operators and its applications
Minicourse of five one hour lectures by
Peter Kuchment
(Mathematics Department, Texas A&M University)
Monday 24 May to Friday 28 May from 10.15 to 11.15 in seminar room S III
Abstract:
The lectures will address properties of periodic elliptic equations in
Rn
or on an Abelian cover of a compact manifold. The main technique
used for studying such operators is the Floquet theory, which looks
significantly different from what one is used to in ODEs. The lectures
will contain an introduction to this theory. Spectral properties of
periodic elliptic operators and properties of solutions of periodic
elliptic equations (e.g., Liouville type theorems), as well as
important applications to solid state physics and optics will also be
discussed.
The inverse option pricing problem
Lecture by Victor Isakov
(Department of Mathematics & Statistics, Wichita State University)
Wednesday 26 May and Thursday 27 May from 11.30 to 12.30
in seminar room S III
Abstract:
We consider the problem of recovery of the so-called volatility
coefficient of the Black-Scholes partial differential equation from
available additional data. We review the current state of the problem,
including available results on the inverse parabolic problems with
final overdetrmination, and describe recent theoretical and numerical
results based on localization properties of its solution.
Statistcal estimation: exploiting non-data information
Lecture by
Roger J-B Wets
(Department of Mathematics, University of California, Davis)
Wednesday 26 May at 14.15
in room G111 of the Chydenia building of Helsinki School of Economics,
address Runeberginkatu 22-24, Helsinki.
Abstract:
Non-parametric estimation of a density function is used as a vehicle
to illustrate the significance to include non-data information in the
formulation of a statistical estimation problem. This, in turn,
raises questions about consistency and other asymptotic properties of
estimators that include such non-data information (shape, support,
moment bounds, etc.). I shall sketch out a "quantitative" consistency
result derived via of a strong law of large numbers for random lower
semicontinuous functions, and describe numerical procedures that are
appropriate for this class of problems.
Introduction to seismic inverse scattering
Lecture by
Maarten
de Hoop
(Colorado School of Mines)
Thursday 27 May from 14.15 to 16.00
in seminar room S III
Quantum graphs and their applications
Lecture by
Peter Kuchment
(Texas A&M University)
Friday 28 May from 14.15 to 15.00
in seminar room S IV
Accommodation
Please see here for information
about accommodation.
math.hut.fi>
26 May 2004