They're called Kazhdan-Luzstig cells. They arise in the study of some fancy-dancy polynomials called Kazhdan-Luzstig polynomials, which are deeply related to the study of Coxeter groups (which can be thought of as algebraic entities that arise from a set of generators and a series of "mirror" or "reflection" identites). roughly speaking, these polynomials can be used to decompose the groups into "cells". Understanding cells is of importance to some crazy mathematicians somewhere (namely, Paul Gunnells, with whom I'm working).
In particular, I was working with a Coxeter group that can be represented geometrically as a tessellation of 3D hyperbolic space with a hyperbolic-tetrahedron determined by dihedral angles (angles between facets) of π/4, π/3, π/3, π/3, π/2, and π/2. The above two cells are entirely composed of reflected tetrahedra with those angles, illustrated in the Poincaré ball model (so the bubbly-bit is like the horizon of their exotic little hyperbolic universe).
The term cell is just used as to indicate a way of subdividing the group of possible reflections based on some algebraic properties that are mysterious to me and of little concern to my end of the research (and of utmost concern to my professor, I think).
I'm basically being paid lots of money to learn the geometry end of things and make some pretty pics of very confusing and elaborate three dimensional structures, which represent something far more abstract.
Based on online tests that I took while highly distracted, 136-138 (thus, I'm not a genius). But IQ tests are solvable in nature, and if one wanted to convince the world that they had an arbitrary IQ within some reasonable pad of their actual abilities, it could certainly be done with a bit of practice.
I might come galavanting back home again next week, if you're interested in some chill time. But I still think you should come to Noho! I have to bike there a few times in the near future anyway, and there's a great Moroccan food joint that you must try!
Moroccan food would kill me with my IBS! How about this? How about a hang out in Spfld and then one in Noho closer to my birthday so I havw some more money to spare to get up there and treat myself to gifts! :]
Sounds good. I'm trying to arrange a return to the field come next week, though I have to balance it with potential meetings for finalizing this research affair, and catching up with the professor for the GRad course I'm trying to enroll in.
And the Moroccan food might actually not kill you; they have many options on the menu, including a variety of vegetarian and vegan things. I have mild IBS from dairy, soy and other things, but I've had some fairly non-threatening bites from there and an associated Mediterranean joint near my brother's apt.
Speaking of which, Jeff is touring with his band starting tomorrow. When he gets back I'll get ahold of some of their music; it's pretty damn good.
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In particular, I was working with a Coxeter group that can be represented geometrically as a tessellation of 3D hyperbolic space with a hyperbolic-tetrahedron determined by dihedral angles (angles between facets) of π/4, π/3, π/3, π/3, π/2, and π/2. The above two cells are entirely composed of reflected tetrahedra with those angles, illustrated in the Poincaré ball model (so the bubbly-bit is like the horizon of their exotic little hyperbolic universe).
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I'm basically being paid lots of money to learn the geometry end of things and make some pretty pics of very confusing and elaborate three dimensional structures, which represent something far more abstract.
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http://www.facebook.com/album.php?aid=2028402&id=209600755&l=15947bf5b9.
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I love the first picture. However, you are too smart to be my friend and I think your IQ is above the 130's.
LYLAS,
Steph ;]
Anyways..you know I love you. You are bloody brilliant my dear. Smartest person I know by far. Miss you so much!
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I might come galavanting back home again next week, if you're interested in some chill time. But I still think you should come to Noho! I have to bike there a few times in the near future anyway, and there's a great Moroccan food joint that you must try!
Lylab!
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And the Moroccan food might actually not kill you; they have many options on the menu, including a variety of vegetarian and vegan things. I have mild IBS from dairy, soy and other things, but I've had some fairly non-threatening bites from there and an associated Mediterranean joint near my brother's apt.
Speaking of which, Jeff is touring with his band starting tomorrow. When he gets back I'll get ahold of some of their music; it's pretty damn good.
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