Functional Analysis/Operator Algebras Seminar, Winter 1999
- Date: 1/8/99
- Speaker: Mihai Putinar, UCSB
- Title: Introduction to the cohomology of topological algebras I
- Abstract:
We will give an an introduction to
the Hochschild cohomology of Frechet modules over Frechet
algebras, with emphasis on the first three cohomology groups
which have intrinsinc meanings and special interest. We will
present various examples mainly from differential and
algebraic geometry.
- Date: 1/15/99
- Speaker: Mihai Putinar, UCSB
- Title: Introduction to the cohomology of topological algebras II
- Date: 1/22/99
- Speaker: Bjorn Gustafsson, Royal Institute of Technology, Stockholm
- Title: Vortex motion in two-dimensional hydrodynamics
- Abstract:
We study the motion of finitely many point vortices
in a two-dimensional fluid region of arbitrary geometry.
The fluid is supposed incompressible and non-viscous.
In the case of only one vortex, it interacts with the walls in such
a way that it (typically) moves in a periodic manner along a closed
curve. For two or more vortices there are interactions also between the
vortices, and the motion may be very complicated (“chaotic”). The
system may even break down in a finite time due to collisions. An
explicit example of a collosion between three vortices was given by
Y. Kimura in 1988.
However, Martin Flucher and myself have shown a couple of years ago that,
in the case of just two vortices, collisions can never occur. The proof
of this is based on a detailed study of the Green’s function of the domain.
- Date: 1/29/99
- no meeting
- Date: 2/5/99
- Speaker: Mihai Putinar, UCSB
- Title: Introduction to the cohomology of topological algebras III
- Date: 2/12/99
- Speaker: Anne Louise Svendsen
- Title: On the notion of amenability for groups
- Date: 2/19/99
- Speaker: Bernie Russo, UC Irvine
- Title: Jordan approach to representations of the Lorentz group
- Abstract:
The Canonical Anticommutation Relations are formulated in the
context of Banach Jordan triple systems. They are used to construct in an
elementary way a spin factor structure on finite dimensional complex
Euclidean space and a subgroup of the corresponding linear isometry group.
Some representations of the rotation and Lorentz group which are analogous
to spinor representations are realized in this group and its Lie algebra.
- Date: 2/26/99
- no meeting
- Date: 3/5/99
- Speaker: Dietmar Bisch
- Title: Planar algebras and subfactors
- Abstract:
Subfactors with finite
Jones index have an amazingly rich mathematical structure and an interplay
of analytical, algebraic-combinatorial and even topological techniques
is intrinsic to the theory.
A subfactor can be viewed as a group-like object that encodes what
one might call generalized symmetries of the mathematical or physical
situation from which it was constructed. To decode this information
one needs to compute a system of inclusions of certain finite dimensional
C$^*$-algebras naturally associated to the subfactor. This structure can
be described as a planar algebra, that is a graded vector space
whose elements are represented by labelled n-boxes which can be
combined in planar, but otherwise quite arbitrary ways.
This allows one to employ a diagrammatic language to manipulate
certain operators on a Hilbert space associated to a subfactor and to carry
out intricate calculations using topological arguments.We will discuss the notion of planar algebras and present some examples
such as the Temperley-Lieb and Fuss-Catalan algebras.
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