The UVM Department of Mathematics and Statistics is proud to present the Algebra and Number Theory Seminar (unQVNTS) series:

A Twisted Euclidean Algorithm

with Dr. Senia Sheydvasser, Bates College

Thursday, November 7
3:15 PM-4:15 PM
Lafayette Hall, Room 406.

Abstract: The classic Euclidean algorithm is, of course, thousands of years old. We will consider a twist on this old idea by considering what happens when we replace rings with rings with involution (that is, an antiautomorphism that squares to the identity). Very simple examples of this include rings of quadratic integers (with the Galois conjugate playing the role of the involution); more interesting ones include orders of quaternion algebras closed under some orthogonal involution. In this setting, one can produce a variant of the Euclidean algorithm that allows attacking many of the same problems: unique factorization, producing generators of matrix groups, and constructing fundamental domains for certain hyperbolic groups.

Dr. Senia Sheydvasser website