MAA MathFest 2012 Poster
This poster is published in the February/March 2012 issue of MAA FOCUS.
The image featured on the MAA MathFest 2012 poster is a representation of Cayley’s cubic surface. It is the unique cubic surface having four ordinary double points, the maximum possible for cubic surfaces. Provided courtesy of Bernd Sturmfels (University of California, Berkeley), this rendering of the surface was created by Oliver Labs (Saarland University) using his surfex software.
Sturmfels will be presenting the Earle Raymond Hedrick Lectures at MAA Mathfest, Aug. 2-4, in Madison, Wisconsin. Abstracts of his talks are below.
MAA MathFest 2012: Earle Raymond Hedrick Lecture Series
Bernd Sturmfels, University of California Berkeley
Algebraic Geometry: Tropical, Convex, and Applied
Lecture 1. Thursday, 10:30 – 11:20 a.m., Ballroom AB
Abstract: In tropical arithmetic, the sum of two numbers is their maximum and the product of two numbers is their usual sum. Many results familiar from algebra and geometry, including the quadratic formula, the fundamental theorem of algebra, and Bezout's theorem, continue to hold in the tropical world. In this lecture we learn how to draw tropical curves and why evolutionary biologists might care about this.
Lecture 2. Friday, 9:30 – 10:20 a.m., Ballroom AB
Convex Algebraic Geometry
Abstract: This lecture concerns convex bodies with an interesting algebraic structure. A primary focus lies on the geometry of semideﬁnite optimization. Starting with elementary questions about ellipses in the plane, we move on to discuss the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.
Lecture 3. Saturday, 9:30 – 10:20 a.m., Ballroom AB
The Central Curve in Linear Programming
Abstract: The central curve of a linear program is the algebraic curve along which the interior point algorithms travel. We determine the degree, genus, and defining ideal of this curve. These invariants, as well as the total curvature of the curve, are expressed in the combinatorial language of matroid theory. This is joint work with Jesus De Loera and Cynthia Vinzant.