Summary: Research Summary
July 31, 2009
I have tried to make this summary readable by any mathematician, and
the first paragraph of each section mostly readable by any scientist.
First I discuss my past research, and then starting on page 10 my
current research projects. These include discussion of my published
papers relevant to them, namely .
My field is group theory (the study of symmetry) and its applica-
tions outside group theory. For me this has mostly meant applications
in algebraic geometry, some by myself and some jointly with several
different coauthors. Most notable is a long series of papers concerning
the spaces of deformations of various classical geometric objects like
curves in the plane, or cubic surfaces. I have also contributed to a
number of problems in topology and pure group theory, for example
hyperbolic reflection groups and the topology of their associated hy-
perplane arrangements. My work in algebraic geometry and reflection
groups led to my current research project concerning the monster finite
simple group, described in section 6.
In 2006 I began moving into a new field: representation theory. In