# The distribution of the eigenvalues of a random system of homogeneous equations

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Peter Buergisser

created by daniele on 24 Jul 2015

3 sep 2015
-- 11:00

Sala Conferenze Tricerri, DiMaI "Ulisse Dini", Firenze

**Abstract.**

The theory of eigenvalues and eigenvectors of matrices is a well-studied subject in mathematics with a wide range of applications.
However, attempts to generalize this concept from linear to homogeneous polynomial systems of higher degree have only been made recently,
motivated by tensor analysis. We analyze the distribution of the eigenvalues of random systems of polynomial equations (where the
randomness is with respect to the unitary invariant Weyl distribution) and describe the limit distribution when the degree d is fixed and the
number of variables goes to infinity. Joint work with Paul Breiding.