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The permanent and dual varieties

Uffe Heide-Jørgensen
(IMF)
Ph.d.-seminar
Torsdag, 25 februar, 2010, at 16:15-17:15, in Aud. D4 (1531-219)
Abstrakt:
The permanent is an important object in combinatorics and theoretical computer science. At first glance it appears to be rather similar to the determinant - in fact in characteristic 2 they are the same thing - however they are very different.
I will give a brief introduction to what the permanent is and why it is interesting, introducing some terms from complexity theory. Furthermore I will sketch an elementary proof of the fact that the permanent has a quadratic lower bound in determinental complexity.
Passing on to (algebraic) geometry I will introduce dual varieties and motivate why this might be interesting in the study of the determinental complexity of permanents.
Kontaktperson: Magnus Roed Lauridsen