Hello internet! My name is Sam (Lewallen,) and I’m the third member of this intrepid triumvirate. I am interested in everything, though my specialized knowledge is limited basically to topology and geometry, knot theory in particular. I’ve worked on Khovanov homology, and the Volume Conjecture. I’m also hugely interested in neuroscience, i.e., figuring out how the brain works (ooooh consciousness!), and I would love if fancy math ends up playing a role.
I have lots of posts planned. Here are a few:
- Alex and I want to do a series on zeta functions, the different types that there are and how they show up everywhere.
- I, like everyone, am fascinated by the moments when natural numbers pop up in different places, out of the blue. For example, the fact that there are 5 convex regular polyhedra (why 5?!). I want to write a series of posts showing that ALL such “arbitrary” natural numbers can be derived from this 5! Less ambitiously, I want do describe as many situations as possible where this can be done. Any ideas? Here are two: The McKay correspondence says # of polyhedra => number of families of simple Lie algebras; I also think # of polyhedra => # of divsion algebras over . Which then says something about the number of generalized cohomologies you can have, according to some talk by Peter Teichner…
- I have lots of obscure knot theory ideas I want to write about. I want to do overviews of the Alexander and Jones polynomials (and all their various definitions), and discuss some neat ways that they’re related, one, for example, involving random walks on diagrams and zeta functions (#1! #1!)
Do any of these interest anybody? Any other suggestions?
As for my personal info, I’m going to be a G1 at Princeton next year. Anyone gonna be in the area?
Goodbye, dear internet, for now.