Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
Omar Leon Sanchez, Pure Mathematics, University of Waterloo
One of the most interesting applications of (algebraic) Galois theory, and perhaps why it all started, is that it translates the problem of solving polynomials by radicals to group-theoretic questions (in which we sometimes have an easier way to find an answer, e.g. finite groups).
Differential Galois theory (whose founding fathers are Picard, Vessiot and mostly Kolchin) aims to understand the solutions of differential equations by means of the group of differential automorphisms (which has the nice structure of an algebraic group). The Galois correspondence between intermediate differential fields and algebraic subgroups is, as in the algebraic case, the fundamental theorem.
In this talk, we will review the basics of (algebraic) Galois theory. Then we will talk about differential fields and Picard-Vessiot extensions, and finally give an idea of why the ODE x'' + t x = 0 is not solvable by
elementary functions and integration.
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within our Office of Indigenous Relations.