GWU Topology Seminar
Fall 2010 – Spring 2011
March
11, 2011, Friday 5 – 6 pm.
Speaker: Slava Krushkal,
Title: Categorification of spin
networks
Place: Monroe Hall,
Abstract: This
talk will focus on categorification of the Jones-Wenzl projectors (recent joint work with Ben Cooper),
leading to a categorification of spin networks and in
particular of 6j-symbols. I will also discuss specific examples and applications.
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Logic-Topology Seminar
October 20, 2010, Wednesday 5:15 – 6:15 pm.
Speaker: Jozef Przytycki,
GWU.
Title: Homology of distributive structures: from Boolean
algebras to spectral sequences
Place: Monroe Hall,
Abstract: Homology theory of associative structures like groups
and rings
has been zealously studied throughout the past starting
from the work of Hopf,
Eilenberg, and Hochschild, but
non-associative structures, like quandles, were
neglected till recently.
The distributive structures
has been studied for a long time and already C.S. Peirce in 1880 stressed the
importance of
(right)
self-distributivity in algebraic strictures.
However homology for such universal algebras was introduced only
15 years ago by Fenn, Rourke and Sanderson.
I will develop the theory in
the historical context describing relations to topology and similarity with
some structures in logic.
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October 12, 2010, Tuesday 4 – 5 pm.
Speaker: Carl Hammarsten, GWU.
Title: The Mapping Class Group of Orientable
Surfaces II
Place: Monroe Hall,
This is part II of the talk
from last week.
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October 5, 2010, Tuesday 4 – 5 pm.
Speaker: Carl Hammarsten, GWU.
Title: The Mapping Class Group of Orientable
Surfaces I
Place: Monroe Hall,
Abstract: In the topology of three-dimensional manifolds,
one often glues
manifolds together by means of various different
homeomorphisms of their
boundaries. Gluing by isotopic homeomorphisms gives one and the
same result,
so it is therefore reasonable to investigate the group
of homeomorphisms of
a surface onto itself modulo homeomorphisms isotopic
to the identity. The
resulting group is called the Mapping Class Group. By
considering the
slightly more convenient subgroup of homeomorphisms fixed on
the boundary it
can be shown that, for any orientable
surface, this subgroup is generated by
twists along a finite family of simple closed curves. This
is the well-known
Dehn-Lickorish Twist Theorem. We will present an elementary and elegant, yet
self-contained, proof of this theorem.
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September 24, 2010,
Friday 11 – 12 noon (note the unusual time)
[ This is jointly with the Mathematical and Computational
Biology Seminar ]
Speaker: Tamal
Dey, Department of Computer Science,
Title: Computing Homology Cycles with Certified Geometry
Place: Monroe 267, 2115 G Steet.
Abstract: Computation of cycles representing classes of homology
groups is a fundamental problem arising in applications
such as parameterization, feature identification,
topology simplifications,
and data analysis. Variations of the classical Smith
Normal Form algorithm and
the recently developed persistence algorithm
do compute representative cycles of a homology
basis for a simplicial complex,
but they remain
oblivious to the input geometry. Some recent research
in computational topology have addressed the problems
of computing homology cycles that are optimal with
respect to a given metric. In this talk, we concentrate
on two such developments: (i)
Computing an optimal
basis for one dimensional homology of a simplicial complex
and using it to approximate such a basis for a smooth
manifold from its point data; (ii) Computing an optimal
cycle homologous to a given cycle in a simplicial
complex.
We provide efficient
algorithms with their guarantees for (i)
and show that classical Linear Programs can solve (ii)
for some interesting cases even though the general
problem is NP-hard.
Biography: Tamal K. Dey is professor of computer science
at the
includes computational geometry, computational topology and
their applications in graphics and geometric modeling.
After finishing his PhD from
in 1991 he spent a year in
as a post doctoral fellow. He has held academic
positions
in Indiana University-Purdue
University at Indianapolis,
Indian Institute of Technology, Kharagpur,
a book ``Curve and surface reconstruction: Algorithms
with
mathematical analysis" published by Cambridge University
Press.
He leads the Jyamiti group which has developed
various software including the well known Cocone software
for surface reconstruction and DelPSC
software for
mesh generation. Details can be found at
http://www.cse.ohio-state.edu/~tamaldey.
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Some Previous Topology Seminars: