(2019.09.11 14:00pm N205)Nikolai Vassiliev:Monomial combinatorics of polynomial ideals

Time:2019-09-06  Source:

Title:          Monomial combinatorics of polynomial ideals

Speaker:        Prof. Nikolai Vassiliev (St. Petersburg Department of Steklov Institute of Mathematics)

Time&Venue:     2019.09.11  14:00pm  N205

Abstract::      The talk will be devoted to applications of combinatorics of some objects defined by supports of polynomials of polynomial ideals to the theory of Groebner bases, tropical bases, involutive theory and torical ideals. Polynomials from the universal Groebner basis will be described in terms of intersections  dimensions of the linear hulls of monomials from young diagrams  with the supports of polynomials  and the ideal itself. The
concept of an extended Groebner bases will be introduced and some finiteness theorems connected with  the combinatorics of the set of multidimensional young diagrams will be discussed. We will discuss the problem of complexity of building a tropical basis of a polynomial ideal as well as some problems related to finding polynomials in an ideal having a support with a fixed number of elements, binomials for example.