Monomial combinatorics of polynomial ideals
副标题:
时间:2019-09-06 来源:
题目: Monomial combinatorics of polynomial ideals
报告人: Prof. Nikolai Vassiliev (St. Petersburg Department of Steklov Institute of Mathematics)
时间地点: 2019.09.11 14:00pm N205
摘要: 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.