March 13, 2004

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

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Re: Number Theory and Physics

Is it possible to briefly explain what the sentence

Well, we want to be able to count the points on the Calabi-Yau, defined over the finite field $F_{p^k}$.

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?)

Posted by: Urs Schreiber on March 16, 2004 3:49 AM | Permalink | PGP Sig | Reply to this

You can’t (easily) send a trackback from a comment.

You can, however, trivially send a trackback from a blog post: just link to my post, and — through the magic of trackback auto-discovery — your post will send a trackback to mine.

I found today’s talks (the ones I was able to attend) at A&M rather depressing.

Perhaps I will find the energy to write up my thoughts some other time.

Posted by: Jacques Distler on March 16, 2004 11:33 PM | Permalink | PGP Sig | Reply to this