The Graduate Student Seminar

is pleased to announce a lecture by

Brittany Noble

on

$p$-Colorability of Knots

Tuesday, October 31 at 4pm in JR 202

Abstract:

A knot $K$ is $p$-colorable for a prime number $p$, if each strand of a projection of $K$ can be assigned a number (called a ``color'') from the set $\{0,1,\dots,p-1\}$ such that (i) at least 2 colors are used, and (ii) and at each crossing if $y$ and $z$ are the colors of the understrand , and $x$ is the color of the overstrand, then $2x-y-z=0\mod p$. A brief introduction into knot theory will be given along with a theorem that determines the $p$-colorability of any $(m,n)$ torus knot.

Brittany Noble received her undergraduate degree in mathematics from CSUN.She is currently a second year graduate student at CSUN and a FERMAT Fellow. Her talk is based on work for her thesis with Prof. Magnhild Lien.