Algebra & Combinatorics Research Group  |  Texas A&M University





A&C Seminar

Working Seminar
   in Algebra

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A&C Seminar:  Fall 2008, Fridays, Milner 317, 3:00–3:50 p.m.

September 19 Stefan Forcey (Tennessee State University)
3:00–3:50 Positrons, polytopes, and antipodes.
Abstract:   The process of renormalization lets us use Feynman diagrams to calculate the precise strengths of many forces of nature, despite the suspicious subtraction of infinities. Kreimer and Connes found a way to mathematically model the process using the antipode of a graded Hopf algebra. Their algebra turns out to be fundamental in mathematics as well as physics, as part of a larger family of algebras based on combinatorial structure. I'll show a new pictorial way of looking at that family and its inner relations. Then come introductions of new family members and lots of questions about how they fit in. One question is about the significance of the fact that these algebras, new and old, all come from the vertices of convex polytopes! If time permits we can go on to discuss multicolored versions and potential modules over the algebras already introduced.