Frontiers in Mathematical Sciences
7th Conference University of Isfahan  January 13, 2020 
Title:
Bounds on vector fields: degrees and generators
Speaker:
Seyed Hamid Hassanzadeh, Federal University of Rio de Janeiro
Date, Time, and Venue: Thursday, January 2  09:0009:45  Hall 2
Abstract:
Finding algebraic integrals of a vector field is a fascinating question. Over a century ago Poincare had been interested in this question. Besides this fact, it is not clear what he might have asked about the algebraic integrals! The question of finding the minimum degree of a vector field which leaves a variety of invariant has had significant progress in the recent years. In this talk which is a report on ongoing work, we present a Commutative Algebraic point of view to the object. We show that the ainvariant of a ring is the numerical invariant that can unify and explain several previous results such as some in [Cerveau, Lins Neto, Esteves, Soares]. We determine lower bounds, upper bounds and bounds on the number of the generators of the module of non trivial vector fields which leave a curve invariant.
This is based on a joint work with: M. Chardin, C. Polini, A. Simis, and B. Ulrich
