G. Milton Wing Lecture Series
Prof. Bernd Sturmfels of the University of California, Berkeley, will give a series of three talks.
Wednesday, April 8, 4:50 - 6:00 p.m. in Hoyt Auditorium
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.
Beyond Linear Algebra
Thursday, April 9, 1:00 - 2:00 p.m. in Goergen 108
Linear algebra is the foundation of scientific computing and its numerous applications. Yet, the world is nonlinear. In this lecture we argue that it pays off to work with models that are described by nonlinear polynomials, while still taking advantage of the power of numerical linear algebra. We offer a glimpse of applied algebraic geometry, by discussing current trends in tensor decomposition, polynomial optimization, and algebraic statistics. Students will especially enjoy the illustrations of these concepts by many colorful pictures.
Friday, April 10, 1:00 - 2:00 p.m. in Goergen 108
Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, generalizing those of toric varieties and their moment maps. Another special class, including Gaussian graphical models, are varieties of inverses of symmetric matrices satisfying linear constraints. We present a general theory of exponential varieties, with focus on those defined by hyperbolic polynomials. This material appeared in a recent paper with Mateusz Michalek, Caroline Uhler, and Piotr Zwiernik.