Geometry Seminar

Date: January 22, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Frank Sottile, TAMU

Title: Newton-Okounkov Bodies for Applications

Abstract: Newton-Okounkov bodies were introduced by Kaveh-Khovanskii and Lazarsfeld-Mustata to extend the theory of Newton polytopes to functions more general than Laurent polynomials. This theory has at least two implications for applications. First is that Newton-Okounkov bodies provide an approach to counting the number of solutions to systems of equations that arise in applications. Another is that when the Newton-Okounkov body is an integer polytope (there is a Khovanskii basis), there is a degeneration to a toric variety which in principal should give a numerical homotopy algorithm for computing the solutions. This talk will sketch both applications.