Colloquium: New Methods in Effective Algebraic Geometry, Martin Helmer, University of Copenhagen
Kontakt: erik [dot] wahlen [at] math [dot] lu [dot] se
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At its most basic algebraic geometry studies algebraic varieties, that is the solution sets of systems of polynomial equations. In this talk our focus is on practically effective computational methods to answer questions about the structure and geometry of algebraic varieties. Gröbner basis have been used quite successfully to answer many questions in this area, however for large examples the computation of a Gröbner basis can become impractical. In this talk we will discuss two recent results that give rise to effective computational methods which do not require the computation of a Gröbner basis. The first result uses polyhedral combinatorics to study both a constrained optimization problem and the geometric properties of a large class of algebraic varieties. The second result leads to a new technique to test if one variety is contained in another.