Research:My training is in algebraic geometry (PhD, Brown, 1981), but I also have significant background in computer science and subjects related to aviation. I have a strong interest in applications of algebraic geometry and representation theory in coding and cryptography.
Computational Complexity of Quadrature Rules. I am applying concepts from information theory to develop new algorithms for estimating the Riemann integral of a function defined by a table of values.
- Information Theoretic Schottky Problem. I am studying the statistical properties of period matrices of complex algebraic curves to determine to what extent the distribution of the periods determines (1) whether the matrix is in fact a period matrix [Schottky Problem] and (2) properties of the curve [Torelli Problem].
- Theta Divisors in Moduli Spaces of Vector Bundles and Automorphism Groups of Curves. I have several results in this direction, but the project is not mature enough to be written up.
- Using Turbulence to Fly Faster. A development of and analysis of "relative dolphin flight" for powered aircraft.
Other Recent projects
Linear Codes from Schubert Varieties. Much of this is joint work with Sudhir Ghorpade.
- Analytic Computation of Some Automorphism Groups of Riemann Surfaces, Kodai Mathematical Journal, 30 (2007), 394 ĘC 408.
Home page: http://www.isu.edu/~wolpjame/