People
David Ishii Smyth
Associate Professor
Contact Info:
Tufts University
Department of Mathematics
503 Boston Ave
BromfieldPearson
Room 217
Medford, MA 02155
Email @tufts.edu: david.smyth
Phone: 6176272630
Expertise:
Algebraic Geometry
Research:
My area of research is algebraic geometry, the application of
geometric methods to understand solutions of systems of polynomial
equations. In linear algebra, one learns algorithms for explicitly
describing the solutions of a system of linear polynomial equations.
When considering nonlinear equations however, such explicit
descriptions are usually impossible to obtain. But we can still gain
important insights by investigating geometric properties of the
solution set. For instance, is it smooth or singular? How many
connected components does it have? Perhaps surprisingly, these
simple questions lead to a rich and sophisticated theory, with deep
connections to other areas of mathematics, including commutative
algebra, topology, and complex analysis.
Within algebraic geometry, I am especially interested in curves,
singularities, and moduli theory. More specifically, my research
aims to establish a systematic construction and classification of
geometric compactifications of the moduli space of algebraic curves,
and to develop the technical tools needed to study the geometry of
these compactifications. While I view this work as fundamental in
its own right, it is also important on account of its connection
with theoretical physics. A major impetus for recent work in
algebraic geometry has been the construction of mathematically
rigorous models for ideas from string theory, and compactifications
of the moduli space of curves arise naturally in this context.
