Seminar Event Detail

Group, Lie and Number Theory

Date:  Monday, March 05, 2018
Location:  4088 East Hall (4:10 PM to 5:30 PM)

Title:  The arithmetic of arithmetic Coxeter groups

Abstract:   In the 1990s, John H. Conway developed a visual approach to the study of integer-valued binary quadratic forms. His creation, the "topograph," sheds light on classical reduction theory, the solution of Pell-type equations, and allows tedious algebraic estimates to be simplified with straightforward geometric arguments. The geometry of the topograph arises from a coincidence between the Coxeter group of type (3, infinity) and the group PGL(2,Z). From this perspective, Conway's topograph is the first in a series of applications arising from coincidences between Coxeter groups and arithmetic groups. In this talk, I will survey Conway's results and generalizations arising from arithmetic hyperbolic Coxeter groups.


Speaker:  Marty Weissman
Institution:  UC Santa Cruz

Event Organizer:   Stephen Debacker   


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