MINDS & CIS Fall Seminar Series: Josué Tonelli-Cueto, “Condition numbers and probability for explaining algorithms in computational geometry”

/ August 19, 2022/

When:
September 6, 2022 @ 12:00 pm – 1:15 pm
2022-09-06T12:00:00-04:00
2022-09-06T13:15:00-04:00

Tuesdays, 12pm-1:15pm

Held virtually in person at Clark 110 & over Zoom

Abstract: Complexity analyses of algorithms should help us to understand which algorithms we use when facing a particular computational problem. However, not always do our theoretical complexity analyses reflect the state of the art in practice. In this talk, we aim to show how condition numbers and probability can provide such an explanation for several existing algorithms. We showcase this complexity framework in computational (algebraic) geometry. More concretely, we show more detailedly how it helps explain the practical behavior of two algorithms used in practice: the Plantinga-Vegter algorithm for producing piecewise linear approximations of curves and surfaces, and the Descartes solver for finding the real roots of a real univariate polynomial.

Biography: Josué Tonelli-Cueto is a postdoctoral researcher at UT San Antonio. Before that, he was an FSMP postdoctoral fellow at Inria Paris and the IMJ-PRG from 2020 to 2022. He received his PhD from the Berlin Mathematical School and the Technische Universität Berlin in 2019. His research focuses on the probabilistic complexity of numerical algorithms, particularly in numerical algebraic geometry.

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