Colloquia
Upcoming Colloquiums
Location: Surge 284
Time: 4:10 - 5:00pm
Light Refreshments Served
April 2, 2008
Dr. John Armstrong
Tulane University
"Coloring, Quandles and Categorifications"
Can you color the arcs of a knot diagram red, green, and blue so that at each crossing either all of the colors show up, or none of them do? How many ways can you do it? Does the diagram matter, or just the knot type? Most importantly, can we generalize these questions? Coloring numbers are one of the simplest combinatorial invariants of knots and links to desribe. And with Joyce's introduction of quandles, we can understand them more algebraically. But can we extend these invariants to tangles - knots and links with free ends? Indeed we can, once we "categorify"! Starting from the definition of coloring numbers, we will categorify them and establish this extension to tangles. Then, decategorifying will leave us with matrix represenatations of the monoidal category of tangles.