NEW YORK SEMINAR ON GENERAL TOPOLOGY AND TOPOLOGICAL ALGEBRA
February - May 2009
CHECK FOR CAMPUS AND LOCATION
MAY 7: Strashimir Popvassilev, The City College, CUNY, "On the number of
inscribed squares in a simple closed curve in the plane"; at Baruch College Vertical Campus,
Lexington Avenue and 24th Street. Tea 3:15 p.m., talk 4:00 p.m., Math. Conference Room, 6-215.
For more information, contact A. Todd, artodd@panix.com.
ABSTRACT: It is an old question of Toeplitz if for every
simple closed curve in the plane there are four points on the curve that form the vertices of a
square. Such a square is called inscribed even though it need not be contained inside the curve.
The answer is positive for convex curves, analytic curves, differentiable curves and polygons in
general position (results by various authors), and we review some of the known results. We
present an example that shows that for every positive integer n there is a simple closed curve
in the plane that has exactly n inscribed squares: Our example is differentiable and convex.
We discuss some related natural conjectures.
==================================================================================
MAY 14: Frederic Mynard (Georgia Southern University), "Preimage-wise
function space topologies", at CCNY. Tea 3pm, NAC 8/133, talk 4pm NAC 4/205. For more
information and parking: R. Kopperman, rdkcc@ccny.cuny.edu
.
ABSTRACT (Based on joint work with S. Dolecki and F.
Jordan): Each topology A on the lattice O(X) of open subsets of a topological
space X induces a topology A(X,Y) on the set C(X,Y) of continuous functions from X to Y.
The Isbell, compact-open and point-open topologies are instances. We consider the interplay
between properties of the topology of X and the topologies A and A(X,Y), with a special emphasis
on A(X,R). In particular, we study when A(X,R) is a group topology and show that we can find a
vector space topology A(X,R) strictly finer than the compact-open topology.
==================================================================================
APRIL 23: Ethan Akin, City College, CUNY, "Fractals a la Furstenberg and
Gromov", at CCNY. Tea 3pm, NAC 8/133, talk 4pm NAC 4/205. For more information, parking:
R. Kopperman, rdkcc@ccny.cuny.edu.
ABSTRACT: Furstenberg introduced a dynamic
notion of fractal that we will expound upon and characterize. We will then compare it to what
we call a Gromov fractal (with a name like that it has to be good).
==================================================================================
MARCH 5: Homeira Pajoohesh, Medgar Evers College, CUNY, "Intrinsic
generalized metrics on lattice ordered groups", at CCNY. Tea 3pm, NAC 8/133, talk 4pm,
NAC 4/205. For more information, parking: R. Kopperman,
rdkcc@ccny.cuny.edu.
ABSTRACT: Charles Holland showed that the
intrinsic metrics from a lattice ordered group to itself are exactly the functions of the
form d(x,y)=n|x-y| for some integer n, and that for n\geq1, the triangle
inequality for these functions occurs if and only if the group is abelian. In this talk we
introduce intrinsic partial metrics and intrinsic quasimetrics, and we discuss similar
representations for intrinsic partial metrics and quasimetrics on lattice ordered groups.
==================================================================================
MARCH 19: Strashimir Popvassilev, The City College, CUNY, "Base-base
paracompactness and related properties." At CCNY. Tea 3pm, NAC 8/133, talk 4pm NAC 4/205.
For more information, parking: R. Kopperman,
rdkcc@ccny.cuny.edu.
ABSTRACT: Totally paracompact spaces were
introduced by R. Ford, who proved that ind X = Ind X for totally paracompact metric spaces.
A space X is totally paracompact if every basis for X has a locally finite subcollection
covering X. John E. Porter and the speaker in their dissertations introduced related properties: base-base paracompact,
base-cover paracompact and base-family paracompact. A space is base-base paracompact if it has
an open base B such that every base B' contained in B has a locally finite subcover. This is a
weaker property than total paracompactness: It is known that the irrationals are not totally
paracompact even though every metric space is base-base paracompact. We study relations between
these properties, and in particular the open problem if every paracompact space is base-base
paracompact. For subspaces X of the Sorgenfrey line, X is base-cover paracompact iff F-sigma,
but we do not know whether all subspaces of the Sorgenfrey line, e.g. the irrationals, are
base-base paracompact.
==================================================================================
MARCH 26: Guram Megreshivili, New Mexico State University, "Compact
Hausdorff spaces, Smirnov's theorem, and Stone duality." At Baruch College, Vertical Campus,
Lexington Avenue and 24th Street. Tea 3:15, talk 4:00 p.m., rooms to be arranged. For
more information, contact A. Todd, artodd@panix.com.
Abstract to follow in later notice.
==================================================================================
FEBRUARY 19: Floyd Williams, University of Massachusetts,
"Three Tenors: Ramanujan, Rademacher, and Einstein-a convergence of their music".
At Medgar Evers College, talk at 4 p.m. at 1150 Carroll Street, Room 408. Tea follows
at Mathematics Department. For further information, contact Homeira Pajoohesh,
hpajoohesh@mec.cuny.edu.
ABSTRACT: S.A. Ramanujan, an unschooled,
largely self-taught Indian clerk, managed to emerge, in his brief life span, an epochal,
mystical, mathematical genius. His theorems, more than 3000 in number, with a vast array of
mysteriously beautiful and mind-boggling formulas, continue to daze and stupefy the mathematical
world. In this lecture we can attain only a snapshot of this singular Brahmin soul, where we
focus some attention on his work (with G.H. Hardy) on the partition function p(n), on
Rademacher's extension of that work (in the context of negative weight modular forms), and on
applications to black hole solutions to Einstein's field equations, their topological
deformation and entropy. Here we attempt to maintain, for the most part, a general and less
technical discussion of this mix of ideas. The few technical remarks presented will mainly serve
to provide added perspective.
==================================================================================
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
Queens College, Math. (718-380-1832):
G. Itzkowitz
Queens College, Comp. Sci. (718-997-3478): T. Y. Kong
Medgar Evers
(718-270-6125): H. Pajoohesh