Bernd Sturmfels

Bernd Sturmfels were named Clay Senior Scholars at the Park City Mathematics Institute (IAS/PCMI) program on Geometric Combinatorics (July 2004). His public lecture was held on July 20, 2004, and the notes, on Tropical Mathematics, are available here.

Bernd Sturmfels received doctoral degrees in 1987 from the University of Washington, Seattle, and the Technical University Darmstadt, Germany. After two postdoctoral years at the Insitute for Mathematics and its Applications, Minneapolis, and the Research Institute for Symbolic Computation, Linz, Austria, he taught at Cornell University, before joining UC Berkeley in 1995, where he is now Professor of Mathematics and Computer Science. His honors include a National Young Investigator Fellowship, a Sloan Fellowship, and a David and Lucile Packard Fellowship. Sturmfels served as the Hewlett-Packard Research Professor at MSRI Berkeley in 2003/04, and he was a Clay Institute Senior School in Summer 2004. A leading experimentalist among mathematicians, Sturmfels has authored eight books and about 140 articles, in the areas of combinatorics, algebraic geometry, symbolic computation and their applications. He currently works on algebraic methods in statistics and computational biology.

Tropical Mathematics

These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture is the "tropical approach" in mathematics, which has gotten a lot of attention recently in combinatorics, algebraic geometry and related fields. It offers an an elementary introduction to this subject, touching upon Arithmetic, Polynomials, Curves, Phylogenetics and Linear Spaces. Each section ends with a suggestion for further research. The bibliography contains numerous references for further reading in this field.