Number Theory Seminar

Speaker: Keira Gunn, University of Calgary

"Some Problems on the Dynamics of Positive Characteristic Tori."

The real (or characteristic zero) torus is simply R/Z, or the "decimal part" of any real number with operations of addition and integer multiplication.  With the positive characteristic integers defined to be polynomials with coefficients from a finite field, and the positive characteristic reals their Laurent series counterparts, we can similarly construct the positive characteristic tori (each torus dependent on the choice of field).  At first glance there are many similarities to how operations work in both positive and zero characteristic, but these similarities break down quickly upon further inspection, particularly from a view of dynamics on the tori.

In this talk, we will discuss results on some orbital sets and dynamics formulae on the positive characteristic tori, including the Artin-Mazur zeta function and analogous hypothesis for Furstenberg's Orbital Theorem.

MC5403