### Galois Theory in Two Variables

#### Posted by David Corfield

I have just returned from attending three days of the Final Workshop of the Newton Institute *Non-Abelian Fundamental Groups in Arithmetic Geometry* Programme. I was kindly invited by Café visitor Minhyong Kim, whose lecture we discussed a while ago.

While many of talks were well beyond me, I could detect a few glimmers through the mist, and this was greatly helped by some lengthy chats with Minhyong. Out of these discussions I could also see emerge the seeds of a number of philosophy papers – but more of that another time.

After a tricky start, Mihnyong’s own talk I found one of the most approachable. It rises to a crescendo with the idea that we need a Galois theory for polynomials in two variables. Now wouldn’t that make for a wonderful Polymath project for our culture? All kinds of things we hold dear to us at the Café would be involved – nonabelian duality, nonabelian cohomology, the symmetries of pairs of rational solutions in a configuration space linked by a path… And there’s even the hope for higher-dimensional algebraic entities to play a role, as suggested back here.

Could we entice Minhyong to lead an online project?

Posted at December 18, 2009 10:05 AM UTC
## Re: Galois Theory in Two Variables

Very kind of you to suggest this David, although I’m sure my private fantasy is hardly worth the trouble of many people.

Still, I’ll make a small attempt at demystification within a few days, after I arrive in Seoul. I’m off to Heathrow in an hour.