Discrete Optimization Seminar
Harihar Narayanan
Date : 
June 21 (Tuesday), 2005, 14:0015:00

Place : 
Room 206, RIMS

Lecturer: 
Harihar Narayanan
(Indian Institute of Technology, Bombay)

Title : 
An Implicit Duality Theorem and Its Applications

Abstract: 
Duality Theorems of the type (V^{\perp \perp}=V)
are fundamental to many areas of Mathematics.
We present a way to recast such results in an implicit form
when the system has, in addition to `manifest' variables,
other variables which are `latent'. The aim is to economically
(in time and space) build a new system which is `dual' to
the original system in its manifest variables. Such ideas are
useful whenever we have to build `adjoints' of systems.
We also show that `Implicit Duality' gives a fruitful way of
looking at the `hybrid rank problem' for graphs and vector spaces.


