# Seminars & Colloquia Calendar

## Convex Algebraic Geometry of Curvature Operators

#### Renato Ghini Bettiol (Lehman College (CUNY))

Location: ** Hill 705**

Date & time: Tuesday, 22 October 2019 at 2:50PM - 3:50PM

Abstract: I will discuss the structure of the set of algebraic curvature operators of n-dimensional Riemannian manifolds satisfying a sectional curvature bound (e.g., nonnegative or nonpositive sectional curvature), under the light of the emerging field of Convex Algebraic Geometry. More precisely, we completely determine in what dimensions n this convex semi-algebraic set is a spectrahedron or a spectrahedral shadow (these are generalizations of polyhedra where linear programing extends to as semidefinite programming, and are of great interest in applied mathematics and optimization). Furthermore, for n=4, we describe the algebraic boundary of this set as the zero set of an explicit irreducible polynomial.

This is based on joint work with M. Kummer (TU Berlin) and R. Mendes (Univ of Oklahoma).

R. Shapiro Organizer's Page

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

Ziming Shi, Sagun Chanillo, Xiaojun Huang, Chi Li, Jian Song Seminar website Old seminar website

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

Organizer's webpage: Organizer's webpage

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