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July 28, 2013

Minhyong Kim in The Reasoner

Posted by David Corfield

I recently interviewed Minhyong Kim for Kent’s in-house magazine, The Reasoner, where it now appears in the August. As before with Urs, beware the abrupt transition to the following article.

Reading this,

The work that occupies me most right now, arithmetic homotopy theory, concerns itself very much with arithmetic moduli spaces that are similar in nature and construction to moduli spaces of solutions to the Yang-Mills equation,

one could dream of connections to Urs’ work.

Posted at July 28, 2013 8:28 AM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2639

8 Comments & 0 Trackbacks

Re: Minhyong Kim in The Reasoner

The link to the interview doesn’t work.

Posted by: Tom Leinster on July 28, 2013 5:44 PM | Permalink | Reply to this

Re: Minhyong Kim in The Reasoner

Thanks, fixed. The usual lack of ‘http’.

Posted by: David Corfield on July 28, 2013 8:06 PM | Permalink | Reply to this

Re: Minhyong Kim in The Reasoner

The slides for the talk Minhyong gave in Busan are here.

Thus, we are studying

non-abelian gauge theory in arithmetic topology. (Slide 80)

So, is there any way to relate to nLab’s gauge theory?

Is there any relation to what Frenkel described in Gauge theory and Langlands duality?

Posted by: David Corfield on August 3, 2013 8:09 AM | Permalink | Reply to this

Re: Minhyong Kim in The Reasoner

Does anyone here know about the conference in november that mochizuki is going to attend to (organized by Minyong Kim it seems) ?

Posted by: toto on August 16, 2013 5:47 PM | Permalink | Reply to this

Re: Minhyong Kim in The Reasoner

I can’t find where, but Minhyong Kim did say that he didn’t know if Mochizuki would attend. He may have even said that the conference may not go ahead, but my memory on that account is sketchy. Certainly, Mochizuki doesn’t list such a conference in his upcoming travels, and Kim doesn’t list one on any page of his that I could find.

Posted by: David Roberts on August 17, 2013 7:11 AM | Permalink | Reply to this

Re: Minhyong Kim in The Reasoner

In the interview Minhyong says

I should say it’s far from clear that something will happen in November. In any case, I didn’t expect Mochizuki himself to participate.

Posted by: David Corfield on August 17, 2013 8:46 AM | Permalink | Reply to this

Re: Minhyong Kim in The Reasoner

Thanks, David, that was it. I just couldn’t remember where I’d read it!

Posted by: David Roberts on August 19, 2013 4:15 AM | Permalink | Reply to this

Re: Minhyong Kim in The Reasoner

In the interview, Minhyong said

I tend to think of mathematical theorising, reasoning, and experimentation as not very different from the same kind of processes in physics.

I see in his article Arithmetic Applications of the Langlands Program, Michael Harris writes in a similar vein:

The functoriality conjecture is at the heart of the Langlands program and will undoubtedly remain as a challenge to number theorists for many decades to come. Shortly after formulating his program, however, Langlands proposed to test it in two interdependent settings. The first was the framework of Shimura varieties, already understood by Shimura as a natural setting for a non-abelian generalization of the Shimura-Taniyama theory of complex multiplication. The second was the phenomenon of endoscopy, which can be seen alternatively as a classification of the obstacles to the stabilization of the trace formula or as an opportunity to prove the functoriality conjecture in some of the most interesting cases. After three decades of research, much of it by Langlands and his associates, these two closely related experiments are coming to a successful close, at least for classical groups, thanks in large part to the recent proof of the so-called Fundamental Lemma by Waldspurger, Laumon, and especially Ngô.

Details about the following comment are given in the final section of the paper:

…the Langlands program itself is now undertaking a new series of experiments, the most ambitious of which has been proposed by Langlands himself…

Posted by: David Corfield on September 3, 2013 12:15 PM | Permalink | Reply to this

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