Theoretical physics and string theory provide useful hard problems to solve involving polyhedra geometry, computational algebra and computational algebraic geometry. We describe some of these problems, some solutions, and several challenges and open problems for the computational algebra and algebraic geometry community. The work described here is based on joint work with Liam McAllister (Cornell; string theory and cosmology) and several other physicists.
Michael Stillman is a computational algebraic geometer. He received his Ph.D. at Harvard in 1983 under David Mumford, (using macsyma heavily!), and after postdocs at University of Chicago, Brandeis, and MIT, has been at Cornell University in the math department since 1987. In the 1980’s, he wrote with Dave Bayer the computer algebra system Macaulay, and since the early 1990’s has written, with Dan Grayson, a different computer algebra system, called Macaulay2, which is under active development, and has currently about 300 community contributed software packages distributed with the system, and overall 4000 papers referring to Macaulay2.