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May 22, 2008

Workshop: Non-Commutative Constructions in Arithmetic and Geometry

Posted by Urs Schreiber

guest post by Minhyong Kim

This is a reminder to people with reasonable access to London that there will be a workshop on

Non-commutative constructions in arithmetic and geometry

at University College London on 7 and 8 June. Further information can be found on the page

http://www.ucl.ac.uk/~ucahmki/ncc.html

Unfortunately, I couldn’t get enough funding to support general participants. But, as you will see from the directions there, UCL is very easy to reach from St. Pancras station (Eurostar) or Luton airport (EasyJet), and practically next door to Euston station, allowing the possibility of a day trip from many locations.

Although higher categories do not occur as an explicit theme, the discussion should include many points of interest in common with the regulars of the café.

I hope to see you there.

Minhyong Kim

Posted at May 22, 2008 11:53 AM UTC

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6 Comments & 0 Trackbacks

Re: Workshop: Non-Commutative Constructions in Arithmetic and Geometry

I would be curious about what Connes thinks on the Weil group (Tate about it) and Weil’s fascinating remark on the idea of a geometric interpretation of it in his 1951 paper “Sur la theorie du corps de classes”:

“…; il se peut qu’une telle interpretation renferme la clef de l’hypothese de Riemann; il est plausible qu’il convienne de la chercher du cote de la theorie des espaces fibres dont l’importance se fait de plus en plus grande dans tant de branches de mathematiques, topologie bien entendue, mais deja aussi geometrie algebrique, espaces de Hilbert, et bientot sans doute arithmetique. “

, and Weil’s comments on it in his collected works. I learned a few days ago from Friedhelm Waldhausen of that. Connes and Marcolli’s remarks (e.g. p.18, p.9) indicate that they think about it, Morava wrote about it here and I wonder if Lichtenbaum’s Weil-etale topology connects to that too.

Posted by: Thomas Riepe on May 25, 2008 12:06 PM | Permalink | Reply to this

Re: Workshop: Non-Commutative Constructions in Arithmetic and Geometry

Well, I do think Connes thinks about that remark quite seriously. I remember from quite a few years ago a talk where he described hyper-finite Von Neumann algebras as providing an Archimedean analogue of the theory of the Brauer group over p\mathbb{Q}_p. This was also supposed to be related to Weil’s remark, although precisely how, I don’t recall.

Posted by: Minhyong Kim on May 27, 2008 2:14 AM | Permalink | Reply to this

Re: Workshop: Non-Commutative Constructions in Arithmetic and Geometry

Thanks! I found only the links above (and didn’t understand Morava’s text, perhaps someone knows a more detailed exposition?) when searching what happened with Weil’s idea. Exists more on them?

Posted by: Thomas Riepe on May 27, 2008 9:41 AM | Permalink | Reply to this

Re: Workshop: Non-Commutative Constructions in Arithmetic and Geometry

Dear Minhyong, that sounds like an interesting workshop indeed, is there any plan to make some videos of the talks and have them online somewhere later? Or if it’s too diffcult then maybe copies of the slides of each speaker into pdf files?

Posted by: tom on May 27, 2008 9:31 AM | Permalink | Reply to this

Re: Workshop: Non-Commutative Constructions in Arithmetic and Geometry

This may end up as one of my numerous good intentions that get buried by lethargy, but the current plans are to put out a proceeding.

Posted by: Minhyong Kim on May 29, 2008 12:25 AM | Permalink | Reply to this

Re: Workshop: Non-Commutative Constructions in Arithmetic and Geometry

Dear Minhyong, your website seems to be offline.

Posted by: Thomas Riepe on June 16, 2008 4:13 PM | Permalink | Reply to this

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