NAS-Cinvestav Lectures 2007

Conferencistas NAS-Cinvestav Lectures 2007

Bernd Sturmfels(University of California)
Enero 10-11, 2007 12pm.

LECTURE 1: "Algebraic Statistics for Computational Biology"

Abstract: This lecture gives an introduction to a book with this title which was published recently by Lior Pachter and myself. It concerns interactions between algebra and statistics and their emerging applications to computational biology. Statistical models of independence and sequence alignment will be illustrated by means of a fictional character, DiaNA, who rolls tetrahedral dice with face labels "A", "C", "G" and "T".

LECTURE 2:"The Algebraic Degree of Semidefinite Programming"

Abstract: Semidefinite programs are convex optimization problems that generalize linear programming and are very popular among engineers and computer scientists. If the matrices specifying the problem has rational entries, then each coordinate of the optimal solution is an algebraic number. We report on a joint project with Jiawang Nie and Kristian Ranestad which studies the degree of the minimal polynomials of these algebraic numbers. Geometrically, we determine the critical points attained by a linear functional on a fixed rank locus in a general linear space of symmetric matrices. this degree is computed using methods from complex algebraic geometry, including projective duality, determinantal varieties, and their Chern classes.