# Invited Speakers

## Titles and Abstracts

David A. Cox Amherst College Amherst MA, USA |
## Reflections on Elimination Theory
My lecture will survey developments in elimination theory from Newton and Bézout up to modern times. I will discuss the dominance of elimination theory in the 19th century and the challenges it faced in the 20th century with the rise of abstract algebraic geometry. I will also mention the role of the ISSAC community and my own involvement in computational issues with Gröbner bases and geometric modeling. |

Alicia Dickenstein
Universidad de Buenos Aires Buenos Aires, Argentina |
## Positive Solutions of Sparse Polynomial Systems
I will discuss (known and unknown) lower and upper bounds for the number of positive solutions of systems of n sparse polynomials in n variables. I will also focus on the associated algorithmic issues. |

Lek-Heng Lim
The University of Chicago Chicago IL, USA |
## Ubiquity of the Exponent of Matrix Multiplication
The 3-tensor corresponding to the bilinear map that takes two matrices to their product shows up in many areas. We will see that its asymptotic tensor rank gives the computational complexity of the multiplicative operations in any infinite family of semisimple Lie algebras, semisimple Jordan algebras, Clifford algebras, etc; as well as the evaluation of matrix polynomials and rational functions of any fixed degrees. Also, its asymptotic injective norm gives the value of the best constants in Grothendieck inequality, Goemans-William inequality, Nesterov \pi/2-theorem, etc. The first part is joint with Ke Ye, the second with Shmuel Friedland. |