David L Reed, Adjunct Professor
Please note: David has left the Mathematics department at Duke University; some info here might not be up to date.
- Contact Info:
- Research Interests:
My research involves the influence that the geometric and topological properties of algebraic varieties exerts on
their arithmetic. Current projects include using techniques from integrable systems to study rational points on
curves. Soliton Theory provides infinite dimensional Grassmanians asssociated to sheaves over algebraic curves.
In rank 1 these can be used to study torsion points of Jacobians which lie on the Abel embedded image of the
curve. I am interested in higher rank versions of these results. Other interests include the topological properties of
conjugate algebraic varieties such as their rational homotopy type.
History and Philosophy of Mathematics
I am also interested in the structure of mathematical argument.
In my book Figures of Thought I
have discussed texts by various mathematicians from Euclid to
Grothendieck from the point of view of how they went about
organizing and developing subject matters and methods and then
finding suitable notions of completeness and conclusion for their
work. In subsequent papers I have developed these ideas further
in contexts such as the growth of class field theory and the
development of the notion of moduli problems.
Recent Papers in the History and
Philosophy of Mathematics. I will be teaching a Topics in
the History of Mathematics Course in Spring Semester 1997 covering
some of this material. For more information click here