October 19-21: Distinguished Lecture Series - Bernd Sturmfels

Bernd Sturmfels

University of California at Berkeley
Professor of Mathematics, Statistics and Computer Science
will give three lectures:

Convex Algebraic Geometry
October 19, 2011, 4:00 PM
B102, Van Vleck Hall
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.

Quartic Curves and Their Bitangents
October 20, 2011, 4:00 PM
B102, Van Vleck Hall
Abstract:
We present a computational study of plane curves of degree four, with primary focus on writing their defining
polynomials as sums of squares and as symmetric determinants. Number theorists will enjoy the appearance of
the Weyl group E7 as the Galois group of the 28 bitangents. Based on joint work with Daniel Plaumann and
Cynthia Vinzant, this lecture spans a bridge from 19th century algebra to 21st century optimization.

Multiview Geometry
October 21, 2011, 4:00 PM
B102, Van Vleck Hall
Abstract:
The study of two-dimensional images of three-dimensional scenes is foundational for computer vision. We
present work with Chris Aholt and Rekha Thomas on the polynomials characterizing images taken by n cam-
eras. Our varieties are threefolds that vary in a family of dimension 11n-15 when the cameras are moving. We
use toric geometry and Hilbert schemes to characterize degenerations of camera positions.