In 1870 Jordan explained how Galois theory can be applied to problems from enumerative geometry, with the group encoding intrinsic structure of the problem. Earlier Hermite showed the equivalence of Galois groups with geometric monodromy groups, and in 1979 Harris initiated the modern study of Galois groups of enumerative problems. He posited that a Galois group should be `as large as possible' in that it will be the largest group preserving internal symmetry in the geometric problem.
I will describe this background and discuss some work of many to compute, study, and use Galois groups of geometric problems, including those that arise in applications of algebraic geometry.
About the speaker
Dr. Frank Sottile is a Professor of Mathematics at Texas A&M University. He earned his Ph.D. under William Fulton after distinguished studies at Michigan State University, Cambridge, and the University of Chicago. His research areas are numerical algebraic geometry, applications of algebraic geometry, algebraic geometry in spectral theory, real algebraic geometry, algebraic combinatorics, Hopf Algebras, Discrete and Computational Geometry, tropical geometry, spectral theory. Sottile has held fellowships with NSF, the Winston Churchill Foundation, the AMS, and the AAAS. Frank has taught and collaborated globally, from Berkeley and Munich to Lausanne and Stockholm.
