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Recent contributions of algebraic geometry and representation theory to complexity theory

Presented by: 
JM Landsberg Texas A&M University
Date: 
Thursday 17th October 2013 - 09:00 to 10:00
Venue: 
INI Seminar Room 1
Abstract: 
Algebraic geometry and representation theory have been used to prove lower bounds for the complexity of matrix multiplication, the complexity of linear circuits (matrix rigidity), and Geometric Complexity Theory (questions related to the conjecture that P is distinct from NP). Remarkably, these questions in computer science are related to classical questions in algebraic geometry regarding objects such as dual varieties, secant varieties, Darboux hypersurfaces, and classical intersection theory, as well as questions in representation theory such as the Foulkes-Howe conjecture and the asymptotic study of Kronecker coefficients. I will give an overview of my joint work with G. Ottaviani (matrix multiplication), L. Manivel and N. Ressayre (GCT) and F. Gesmundo, J. Hauenstein, and C. Ikenmeyer (linear circuits).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons