# Totally positive view of a computer microchip Topology

## Alexander Postnikov

(UC Berkeley)

Monday, May 7, 2001

3:00 pm

891 Evans Hall

ABSTRACT

We define semiconductor networks, which serve as a model for computer
microchips, and discuss the inverse boundary problem for these
networks. Simply speaking, we answer the question: "To which extent
and how can we identify a computer microchip by boundary
measurements?" Interestingly, the theory of semiconductor networks
generalizes (and simplifies) the recent results of Berenstein, Fomin,
and Zelevinsky on totally positive matrices and double Bruhat
cells. Let us say that a matroid on an ordered set is totally positive
if it can be represented by a real k x n matrix with nonnegative
maximal minors. The combinatorial classes of semiconductor networks
are in one-to-one correspondence with totally positive matroids. A
byproduct of our theory is the complete combinatorial description of
totally positive matroids.
Speaker's contact info: http://www.math.berkeley.edu/~apost/

Last modified: Thu Feb 1 12:51:54 PST 2001