The paper is written with a general mathematical audience in
mind. Since it develops a basic tool, based on simple premises, it
is likely that other authors find it useful.
Does
it describe a new discovery or a new methodology that's useful to
others?
Both. The paper describes methods than can useful for
mathematicians working in different fields. It also provides basic
techniques to deal with singular geometric structures.
Could
you summarize the significance of your paper in layman's terms?
Geometric structures can be divided into two types: singular and
non-singular. For non-singular geometric structures, the points are
all equivalent, and one can compare them using a device called a
"connection," as singular geometric structures points are
not all equivalent to each other. One must therefore be careful in
comparing them. The paper develops, for the first time, a theory of
connections for singular objects.
How
did you become involved in this research?
One of my fields of interest is Poisson geometry, where singular
behavior is typical. I arrived at this line of research while trying
to understand certain global invariants for Poisson manifolds.
Rui Loja Fernandes
Associate Professor
Departamento de Matematica
Institution: Instituto Superior Técnico
Lisbon, Portugal
