Totally positive view of a computer microchip
Alex Postnikov
UC Berkeley
April 11,
4:15pm
refreshments at 3:45pm
2338
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 onetoone
correspondence with totally positive matroids. A byproduct of our theory
is the complete combinatorial description of totally positive matroids.

Speaker's Contact Info: apost at math.berkeley.edu
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