# Colloquium: Galois groups in Enumerative Geometry and Applications

Frank Sottile (Texas A & M University)

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

in a long-term project to compute, study, and use Galois

groups of geometric problems, including those that arise

in applications of algebraic geometry. A main focus is

to understand Galois groups in the Schubert calculus, a

well-understood class of geometric problems that has long

served as a laboratory for testing new ideas in enumerative geometry.

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

in a long-term project to compute, study, and use Galois

groups of geometric problems, including those that arise

in applications of algebraic geometry. A main focus is

to understand Galois groups in the Schubert calculus, a

well-understood class of geometric problems that has long

served as a laboratory for testing new ideas in enumerative geometry.

Building: | East Hall |
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Event Type: | Workshop / Seminar |

Tags: | Mathematics |

Source: | Happening @ Michigan from Department of Mathematics, Colloquium Series - Department of Mathematics |