September 6, 2022

12:00 pm / 1:00 pm


Clark Hall, Room 110

Tuesdays, 12pm-1:15pm

Held virtually in person at Clark 110 & over Zoom

Check for event details:


?Condition numbersand probability for explaining   algorithmsin computational geometry?

JosuéTonelli-Cueto, PhD

Postdoctoral Researcher

UT San Antonio

Abstract:Complexityanalyses of algorithms should help us to understand which algorithmswe usewhen facing a particular computational problem. However, not alwaysdo ourtheoretical complexity analyses reflect the state of the art in practice. Inthis talk, we aim to show how condition numbers and probability can providesuch an explanation for several existing algorithms. We showcase thiscomplexity framework in computational (algebraic) geometry. More concretely, weshow more detailedly how it helps explain the practical behavior oftwoalgorithms used in practice: the Plantinga-Vegter algorithm for producingpiecewise linear approximations of curves and surfaces, and the Descartessolver for finding the real roots of a real univariate polynomial.

Biography:JosuéTonelli-Cueto is a postdoctoral researcher at UT San Antonio. Before that, hewas an FSMP postdoctoral fellow at Inria Paris and the IMJ-PRG from 2020 to2022. He received his PhD from the Berlin Mathematical School and the TechnischeUniversität Berlin in 2019. His research focuses on the probabilisticcomplexity of numerical algorithms, particularly innumerical algebraicgeometry.