| Date: | Wed, 19 Mar 2008 |
| From: | Denis Chebikin |
| Subject: | SPAMS Thursday 5pm in 4-231 |
Hi all,
Tomorrow at SPAMS Alejandro will talk about the Legendre transform and its
relation to connected graphs.
See you there!
Denis
Title: A relation between the Legendre transform and connected graphs
Abstract: It is very well known in combinatorics that given an
exponential generating function for labeled objects, its logarithm is
the generating function for the connected ones. This simple idea is
used in other fields: in basic quantum field theory the partition
function Z of a classical action gives a sum of Feynman diagrams, and
its logarithm gives the series of the connected diagrams.
Interestingly, the story does not stop there. When calculating the
effective action via the Legendre transform, such connected diagrams
are further dissected into their 2-edge connected (1-particle
irreducible) components. This involves trees which in turn are the
simplest connected graphs. If we bring this last step back to
combinatorics what does it mean? The talk will explore this and
another loosely related question.