Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

December 18, 2009

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

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2136

1 Comment & 0 Trackbacks

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.

Posted by: Minhyong Kim on December 18, 2009 1:29 PM | Permalink | Reply to this

Post a New Comment