##### Department of Mathematics,

University of California San Diego

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## Jason Williford

## Graphs Derived from Generalized Kac-Moody Algebras

##### Abstract:

In this talk, we will discuss a family of graphs related to the high girth graphs D(k,q). The graphs D(k,q) were originally constructed by utilizing a bilinear product based on the root system of an affine Lie algebra.? We give a modification of this construction which applies to Generalized Kac-Moody algebras of rank 2. Using these constructions we obtain a new lower bound on the maximum number of edges in graphs without 14-cycles.? This is joint work with Art Terlep.

Host: Jacques Verstraete

### September 13, 2011

### 4:00 PM

### AP&M 7321

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