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Class of 1978 Life Sciences Center

**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.

**NB:** A PDF version of this announcement
(suitable for posting) is also available.

**Abstract: **
This lecture concerns convex bodies with an interesting algebraic
structure. A primary focus lies on the geometry of semideite 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.

**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.