Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Solving Polynomials After Klein: The Theory of Resolvent Degree

Alexander Sutherland
Tuesday, May 14, 2019
5:30 pm - 6:20 pm
RH 306

Talk Abstract:

Solving polynomials is a classical problem. From Abel (1824), we know that the generic degree n polynomial cannot be solved in radicals when n is greater than 4. However, we can still solve polynoimals. Indeed, Bring (1786) provides a formula for the generic quintic using only a square root, a cube root, and an algebraic function now known as the Bring radical. Famously, there is also Klein's solution of the generic quintic (1884), which is based on the symmertires of the icosahedron. In this talk, we will introduce the theory of resolvent degree (led by Farb and Wolfson), which is the modern viewpoint on solving generic polynomials via algebraic geometry and topology. We will then examine Klein's solution of the quintic in this framework and look at what we know about extending the methods of Bring, Klein, and Green (1978) towards giving a complete solution of the generic sextic.

About the Speaker:

Alex is a 3rd year Ph.D student whose research uses tools from topology, geometry, and algebra. He is also one of UCI's Pedagogical Fellows for 2019. Outside of math, he likes to go to concerts and watch college football.

Refreshments:

Pizza will be served after the talk.