Special session on Foundations of Numerical Algebraic Geometry at the Fall 2016 AMS Western Section Meeting at University of Denver in Denver Colorado 8--9 October 2016 Organizers: Abraham Martin del Campo Centro de Investigacion en Matematicas, A.C. abraham.mc@cimat.mx Frank Sottile Texas A&M University sottile@math.tamu.edu Description of the session: Numerical algebraic geometry uses methods from numerical analysis to study algebraic varieties on a computer. It arose as a tool for mechanism design over 30 years ago, and is now becoming a key tool for applications of algebraic geometry and an important part of computational algebraic geometry. With this flowering of the subject and its growing use as a tool in pure mathematical explorations, a number of researchers have been turning their attention to foundational aspects of numerical algebraic geometry. This includes rethinking fundamental algorithms, extending certification, and using it in new ways, such as certifiable computation of monodromy. There are also a growing number of students studying the subject. The purpose of this special session is to gather many of those working on such foundational questions in numerical algebraic geometry together to share their ideas and deepen their connections to each other.