**Date & Time:** Wednesday, February 17, 2016, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:** Martin Kreuzer,

Univ. of Passau, Germany

**Title:** Linear Algebra 1.5

**Abstract:** Most algebraists believe they know Linear Algebra.
The purpose of this talk is
to indicate that this is not necessarily true. We show a substantial amount of little known
basic Linear Algebra and its connection to Algebraic Geometry, in particular to the theory of
zero-dimensional subschemes of affine spaces, and to Computer Algebra, in particular to the
task of solving zero-dimensional polynomial systems. Here are some questions which we will
answer in this talk: What are the big kernel and the small image of an endomorphism? What
are its eigenspaces and generalized eigenspaces if it has no eigenvalues? What is the kernel
of an ideal? What is a commendable endomorphism? And what is a commendable family of
endomorphisms? How is this connected to curvilinear and Gorenstein schemes? And how can
you use this to solve polynomial systems?