The conference was held at Cleveland State University from
August 3, 2009 to August 7, 2009. Photos from the conference
may be found below.
Topology is an ideal mathematical discipline for contemporary problems in
science and engineering. Indeed, Topology was conceived by Poincare
as a necessary ingredient for understanding when differential equations
can be solved and this has led, via de Rham and Morse theories to profound
connections between Topology and Analysis. Topological results,
being based not on precise distances or displacements but rather upon global
features, tend to be very robust and insensitive to noise and various
errors, a useful feature for real-world problems. Now,
through applications to areas such as sensor networks, statistics and
robot motion-planning, it is possible to \emph{see} Topology in
the down-to-Earth (and practical) problems of modern technology.
This CBMS Conference presented 10 lectures
by Professor Robert Ghrist focusing on very recent applications of algebraic
topology and its methods to problems in modern technological areas. In
particular, lectures described how topological results may be used to
show whether or not a sensor network has full coverage over a designated area,
an issue important to national (or industrial) security. A different application
is to the statistics of huge data sets (such as genetics data).
New topological methods strive to identify global topological
characteristics of data sets whose natural homes are
in 30, 40 or 1000 dimensions. Traditional statistical methods are quite limited
when dealing with such monstrous data sets and these new topological methods
hold out hope for a completely new type of statistical analysis. Finally,
in recent years, the subject of configuration spaces has received much
attention in Topology because there are deep interactions between geometry
and homotopy theory. But configuration spaces are also important in practical
areas involving, for instance, robot motion-planning; areas (from space
exploration to industrial work) that are essential for future research and
development. This type of symbiosis between topological methods and practical
application is emblematic of the lecture series.
Most topological concepts and tools have
remained ensconced within Mathematics departments, walled
off from scientists and engineers by a formidable history of specialized
terminology and subtle but non-intuitive algebraic constructs.
The broad goal of these lectures was to interest younger mathematicians and
engineers in pursuing the connections between Topology and applications in
science and engineering, and to demonstrate forcefully the particular blend
of efficacy and beauty that characterizes this budding relationship. Such
interdisciplinary interactions provide a perfect pathway for the achievements
of pure mathematics to make their way from the world of abstraction to the
world of people!
Organizers Peter Bubenik and John Oprea:
Return to Oprea's Homepage