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Linear and semidefinite programming in distance geometry
Algebra & Discrete Mathematics| Speaker: | Oleg Musin, University of Texas at Brownsville, Dept. of Mathematics |
| Location: | 2112 MSB |
| Start time: | Fri, Mar 20 2009, 2:10PM |
In this talk we will discuss the maximal cardinalities of spherical two-distance sets. Using the so-called polynomial method and Delsarte's method these cardinalities can be determined for all dimensions n<40. Recently, were found extensions of Schoenberg's theorem for multivariate positive-definite functions. Using these extensions and semidefinite programming can be improved some upper bounds for spherical codes.