TUESDAY, OCTOBER 5: Peter Nickolas, School of Mathematics and Applied Statistics,
University of Wollongong, "The Character of Free Topological Groups". At C.W. Post
Campus, L.I.U. Tea 3:15, Pell Hall 238; talk 4:00, Pell Hall 242. For parking and more information, contact
Susan Andima, sandima@liu.edu.
ABSTRACT: We aim to analyze the character (the least cardinal of an
open basis at the identity) of the free abelian topological group A(X) and
the free topological group F(X) on a Tychonoff space X. Complete success
in this enterprise would reduce the character to an expression involving
only simple topological invariants, such as cardinal invariants, of the
space X. We can carry out such a reduction satisfactorily in the class of
compact spaces, and in some related classes. The analysis of special
subclasses, such as that of compact metrizable spaces, has special
interest. We will give some background on the structure of the topologies
of A(X) (which is fairly simple) and F(X) (which is very complex), to
allow some sketches of arguments to be given, and in particular to show
how the similarities and the differences between the abelian and the
non-abelian cases arise. This is recent joint work with Mikhail Tkachenko.
OCTOBER 14: Ralph Kopperman, CCNY, "Asymmetric topological algebra; how
and why." At CCNY. Tea 3:15, NAC 8/133; talk 4:00 NAC 4/156. For parking,
contact R. Kopperman,
rdkcc@cunyvm.cuny.edu.
ABSTRACT:
Among reasons to give up the traditional assumption that the
topology on our algebraic structure is Hausdorff are:
examples relevant to computation (such as a study of the space of
closed balls of a Banach space),
setting traditional results in a context (such as the existence of
a set
of left invariant pseudometrics that gives rise to a group topology).
We discuss results and open problems related to these reasons.
OCTOBER 21: Susan Andima, Long Island University, C.W. Post Campus, "An
Asymmetric Ellis' Theorem." At CCNY. Tea 3:15, NAC 8/130; talk 4:00 NAC
4/156. For parking, contact R. Kopperman,
rdkcc@cunyvm.cuny.edu.
ABSTRACT: A group with topology (X,*,T)
is called a `semitopological group' if multiplication is separately continuous,
a `paratopological group' if multiplication is jointly continuous and, of course, a
`topological group' if inversion is continuous as well. In two classic
papers of 1957, Robert Ellis proved, for locally compact Hausdorff spaces,
that every paratopological group is a topological group and then, a few
months later, that every semitopological group is a topological group. We
show:
Whenever (X,*,T) is a locally skew compact
semitopological
group, then (X,*,T) is a paratopological group and inversion
is a homeomorphism between (X,T) and (X,Tk).
This generalizes the Ellis theorems, because each locally compact
Hausdorff topology is its own k-dual, Tk, and is a locally skew compact
k-space.
OCTOBER 28: Chyi-Jou Gau, CUNY Graduate Center and Queens College,
"Minimal non-simple sets on 3D and 4D geometric grids". At CCNY. Tea
3:15, NAC 8/133; talk 4:00 NAC 4/113. For parking, R. Kopperman,
rdkcc@cunyvm.cuny.edu.
ABSTRACT: Ronse
introduced the concept of a minimal non-simple ("MNS") set of a binary
image; if no iteration of a thinning algorithm can ever delete a MNS set
then this proposed algorithm "preserves topology". Ronse, Kong, Hall, Ma
and other authors have solved the problem of finding all the MNS sets for
2D and 3D Cartesian grids, 2D hexagonal grids.
We solve the problems of finding all the
MNS sets in (18,12)-, (12,18)- and (12,12)-images on 3D Face-Centered Cubic Grid,
and in (80,8)- and (8,80)-images on 4D Cartesian Grid. Based on the attachment sets of
1's in binary images (introduced by Dr. Kong), we will give a more
detailed account of the behavior of the deletion of a MNS set as well as
the deletion of a non-simple xel. This approach involves continuous
deformation and it is independent of the dimensionality and the shape of
the xels.
NOVEMBER 4: T. J. Peters, University of Connecticut, "Computational
Topology for Reconstruction of Manifolds With Boundary (with Potential
Application to Prosthetic Design)". At College of Staten Island; tea 3:15
1S/215, talk 4:00 1S/111. For parking contact P. R. Misra, (718)982-3626,
prmisra@netzero.net.
ABSTRACT: Algorithms for piecewise linear
approximation of manifolds from sampled data points have become prominent
in the literature. Necessarily, there must be constraints upon the density
of the sampling to yield acceptable results, where topological fidelity is
an important criterion. Often there has been a simplifying assumption that
the surface has no boundary. This talk will present emerging work to show the
importance of rigorous treatment of boundaries, with suggested use in prosthetic design.
The talk is intended to be generally accessible, with the differential
topology and geometry concepts illustrated with graphical images.
NOVEMBER 11: Denis Blackmore, New Jersey Institute of Technology, "Computational
Topology: Where's the Topology?". At Baruch College Vertical Campus,
Lexington Av. between 24th and 25th Street; Tea 3:15 in Room 6-215, talk 4:00
in Room 6-145. For local information contact A. Todd,
artbb@cunyvm.cuny.edu.
ABSTRACT: Computational topology
is a new field that offers many opportunities for productive collaboration
between mathematicians and computer scientists. The focus is on developing
computer-aided methods for determining the stability and consistency of
computational representations of geometric objects in the context of the
topological, piecewise linear, embedding, and differential topological
categories, among others.
In this talk, some fundamental concepts in
and problems arising from computational topology will be described with emphasis
on the topological category. A primary problem in the area is that of developing
algorithmic tests for topological or topological embedding equivalence. This and other
essential aspects of the field will be illustrated with results from our
current research on the computational topology of a special class of
objects called swept volumes. A number of applications highlighting
topological features, including virtual sculpting, virtual surgery, and
modeling biomaterials such as bones will also be discussed.
DECEMBER 9: Lew Ludwig, Denison Univ., "Nagata-Smirnov revisited: Spaces
with \sigma-weakly hereditarily closure preserving bases".
University of Connecticut at Stamford, Tea 4pm, Room 217; talk
5pm, Room 217. Directions can be found at the site
http://www.stamford.uconn.edu/about/mapst.html. For
more information, contact V. Menon, professormenon@hotmail.com.
ABSTRACT:
Burke, Engelking, and Lutzer characterized metrizable spaces as
spaces with a \sigma-hereditarily closure preserving base and indicated
that there is a non-metrizable space that has a \sigma s-weakly
hereditarily closure preserving (\sigma-wHCP) base. In this talk, we
discuss the properties of spaces with a \sigma-weakly hereditarily
closure preserving base and give some sufficient and necessary conditions
for spaces with \sigma-wHCP bases to be metrizable.
For more information, contact:
CCNY (212-650-5346): R. Kopperman
College of Staten Island
(718-982-3626): P. R. Misra
Baruch College (212-387-1463): A. Todd
LIU C.
W. Post Center (516-299-2447): S. Andima
Marymount College (914-631-3200): M.
Hastings
Queens College, Math. (718-997-5849): G. Itzkowitz
Queens
College, Comp. Sci. (718-997-3478): T. Y. Kong