CAM Colloquium: 2020-21 Student-Selected Speaker Mauricio Velasco (Universidad de los Andes) - The geometry of sums of squares

Description

Abstract:
This talk will focus on characterizing the multivariate polynomials which are nonnegative on a subset X of \RR^n. I will begin by explaining why this is an important problem in both pure an applied mathematics (allowing us to effectively solve problems in optimization and control but also posing several fundamental geometric questions). Next I will describe some characterizations available when X is an algebraic variety. These characterizations lead to new algorithms and also to deep novel connections between real and complex geometry, which are currently being explored. The results in this talk are joint work with Blekherman, Sinn and Smith.

The talk will be self-contained and accessible to first year graduate students.

Bio:
Mauricio Velasco's research area is applied algebraic geometry. His main areas of interest are the relationship between Classical Algebraic Geometry and other fields: initially Combinatorics, Commutative algebra and symbolic computation and lately also optimization, complexity theory and machine learning. He was an undergraduate at Universidad de los Andes in Colombia and completed a PhD at Cornell University under the supervision of Mike Stillman in Algebraic Geometry. Velasco did postdoctoral work at UC Berkeley under David Eisenbud and Bernd Sturmfels and, after a brief period in industry at Goldman Sachs, became a faculty member at Universidad de los Andes in Colombia, where he has been since 2011.

Zoom Link Access:
This talk will be given via Zoom, and the link is emailed to the CAM Seminar listserv the week of the talk. If you are not on the listserv, please contact Erika Fowler-Decatur to request the link.