University of Notre Dame, USA
Using numerical insights to improve symbolic computations
Numerical algebraic geometry provides a toolbox of numerical methods for performing computations in algebraic geometry. Even though many computations which are performed on a computer using floating-point arithmetic are not certified, they can often be made very reliably using adaptive precision computations. Moreover, there is a wealth of information regarding the original problem which can be extracted from various numerical computation that can be used to improve subsequent symbolic computations to certify the result. This talk will highlight some recent successes of such hybrid numeric-symbolic methods in algebraic geometry.
Jonathan Hauenstein, Associate Professor and Associate Chair of the Department of Applied and Computational Mathematics and Statistics at the University of Notre Dame, is a computational mathematician specializing in numerically solving nonlinear equations. He earned his PhD in Mathematics from the University of Notre Dame in 2009 and joined the faculty at Notre Dame in 2014 after positions at the Fields Institute, Mittag-Leffler Institute, Texas A&M, and NC State University. He has received various awards including DARPA Young Faculty Award, Sloan Fellowship, Army Research Office Young Investigator Program Award, and Office of Naval Research Young Investigator Award as well as research support from the National Science Foundation.