### Number Theory and Physics

There’s a conference going on here at UT on Number Theory and Physics. Victor Batyrev, Philip Candelas, Daqing Wan and Dave Morrison are giving a series of lectures on the connections between Calabi-Yau Manifolds, Mirror Symmetry and Number Theory.

I’m sitting in Dave’s talk right now, and he’s patiently explaining Gauged Linear $\sigma$-Models to the mathematicians. Years ago, he probably would have said, “and now we take the *symplectic reduction*” ( or, more likely, “and now we take the GIT quotient”). Instead, he’s appealing to Lagrangian mechanics: minimizing the scalar potential, modding out by gauge transformations — the usual physicists’ way of thinking these about these things. Earlier in the day, Candelas responded to the question, “Why are we computing the periods of the holomorphic 3-form on a Calabi-Yau?” with, “Well, we want to be able to count the points on the Calabi-Yau, defined over the finite field $F_{p^k}$.”

Role reversal?

Seriously, though, the connections with Number Theory seem to be indicative of something very deep. I have this forlorn hope that if I sit through the lectures, some glimmer of understanding will emerge.

Later in the week, I’ll probably duck down to College Station to catch a bit of the Cosmology and Strings conference at Texas A&M.

Posted by distler at March 13, 2004 4:00 PM
## Re: Number Theory and Physics

Is it possible to briefly explain what the sentence

really means?? (Sorry for being so ignorant.)

BTW, I’d be interested to hear about the latest status of string cosmology.

(Another BTW: How can I make a ‘trackback’, i.e. a comment at the String Coffee Table which becomes linked here in this blog?)