Arcadian Functor

occasional meanderings in physics' brave new world

My Photo
Location: New Zealand

Marni D. Sheppeard

Sunday, June 10, 2007

M Theory Lesson 65

As nosy snoopy noted, these crystal Calabi-Yau papers are really very interesting. I would like to know more about these random partitions. Okounkov has some notes here.

Recall that in Kapranov's non-commutative Fourier transform for three coordinates $x$, $y$ and $z$, it is natural to represent monomials by cubical paths traced out on such melting crystal partitions. The two coordinate case goes back to Heisenberg's original paper, as we have seen. In a modern guise, his sum rule arises in honeycombs, which look a bit like shadows of melting corners.


Blogger Doug said...

Hi Kea,
These references may be related to 2003, Andrei Okounkov, ‘The uses of random partitions‘, especially section 5.2.2 Construction of the minimizer.

I think I have referenced this paper before.
Zur Izhakian, ‘Duality of Tropical Curves‘, 31 pages, 4 figures, 2005
Some figures appear to link to honeycombs?
Tropical is usually an alternative name for Min-Plus Algebra, but Max-Plus is discussed.

Zur Izhakian, ‘Tropical Varieties, Ideals and An Algebraic Nullstellensatz’, 27 pages, 2 figures, 2005

Daniele Alessandrini, ‘Amoebas, tropical varieties and compactification of Teichmuller spaces’, 41 pages, 2005
“... every polynomial relation among trace functions on Teichmuller space may be turned automatically in a tropical relation among intersection forms over the boundary.”

Amoeba (mathematics): “In mathematics, an amoeba is a set associated with a polynomial in one or more complex variables. Amoebas have applications in algebraic geometry“ are also discussed in the above references.

Zur Izhakian,2004, also has ideas about:
Algebraic Curves in Parallel Coordinates - Avoiding the "Over-Plotting" Problem
New Visualization of Surfaces in Parallel Coordinates - Eliminating Ambiguity and Some "Over-Plotting"

June 11, 2007 3:05 PM  

Post a Comment

<< Home