Area of Research: Computational Algebraic Geometry
The intersection of complexity theory and algebraic geometry
is one of my main interests. I view this merging of areas in a
broad sense, so this means that I enjoy employing combinatorial
and number theoretic techniques wherever necessary. For
instance, some of my recent work applies the truth of the
Generalized Riemann Hypothesis to yield new fast algorithms
for determining the existence of rational points on certain
algebraic sets. (The resulting algorithm places the problem
in the polynomial hierarchy, a particularly important family
of complexity classes related to the P=NP question.) Taking
another example, I recently found a simple new bound, in
terms of polytope volumes, on the number
of connected components of a real semi-analytic set.
You can see all my
papers
and find out more about me
