The 2012 Lester J. Senechal Lecture will be given by Donal O'Shea, president of New College of Florida and former vice president for academic affairs and dean of faculty at MHC.
In his lecture, "Singularities: The Next Generation (aka: When is a Cone not a Cone?)," O'Shea will give a non-technical account of what he considers to be one of the most exciting mathematical advances of the last two decades: "... a beautiful new theory that is transforming our understanding of the topology and geometry of complex algebraic singularities.
His abstract in full:
I will provide a non-technical account of what I regard to be one of the
most exciting mathematical advances of the last two decades. It has
been known for over a half a century that near an isolated singular
point, the set of solutions of a polynomial in several variables can be
complicated (it often fails to be a manifold), but not so complicated as
to be inaccessible (it looks like, in the topological sense, a cone
over a lower dimensional manifold, called the link of the singularity).
The associated theorem, and the study of manifolds that occur as links
produced a flowering of deep insights into the structure of
singularities, and is closely related to some of the greatest
achievements of twentieth century mathematics. Until recently, no one
thought to ask whether the set of solutions actually looks like a cone
in any geometrical sense. A few years ago, two Brazilian mathematicians
showed that, once the number of variables is greater than two, the
answer is no. Their work on explanations of this phenomenon, together
with work of other interested mathematicians, point to a beautiful new
theory that is transforming our understanding of the topology and
geometry of complex algebraic singularities. I will explain using two
examples that are accessible to undergraduate mathematics majors, what
is at stake and what the excitement is about.
The Lester J. Senechal Lecture is presented by Mount Holyoke College's Connecticut Valley Mathematics Colloquium.