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December 24, 2012

Category Theory 2013

Posted by Tom Leinster

Every year or two, there’s a major category theory conference. The last one was in 2011 in Vancouver, and the next one is in Sydney from 7 to 13 July 2013.

The invited speakers are:

  • Eugenia Cheng (Sheffield)
  • Pieter Hofstra (Ottawa)
  • Zurab Janelidze (Stellenbosch)
  • Emily Riehl (Harvard)
  • our very own Mike Shulman (IAS)
  • Ross Street (Macquarie)

More information is at the conference website. There, you can also find out about the workshop the week beforehand, which features mini-courses by Marcelo Aguiar, Richard Garner, Scott Morrison, and again Mike Shulman.

Early in the new year, the website will be updated with info on registration and accommodation, and there’ll be a call for contributed talks.

Posted at December 24, 2012 11:35 PM UTC

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Re: Category Theory 2013

The call for talks is now going out. You can submit your abstract at the conference website. The deadline for this is 1 May.

Posted by: Tom Leinster on January 20, 2013 11:10 PM | Permalink | Reply to this

Re: Category Theory 2013

The program is ready to view.

Hmm, does the ‘conjectural Monster 2-group’ mentioned in Nora Ganter’s abstract have anything to do with the bold prediction made way back when?

sporadic groups are not groups, they are representatives of some wider class of objects

Are there any hints towards the nature of this wider class of objects? What could they be? Groupoids, 2-groups, group objects internal to some unusual ambient category, maybe?

Posted by: David Corfield on June 22, 2013 5:31 PM | Permalink | Reply to this

Re: Category Theory 2013

So, what’s the verdict? What is the Monster 2-group?

Posted by: David Corfield on July 17, 2013 10:50 AM | Permalink | Reply to this

Re: Category Theory 2013

I went to Nora’s talk, but unfortunately I didn’t catch the definition.

Posted by: Tom Leinster on July 18, 2013 4:27 AM | Permalink | Reply to this

Re: Category Theory 2013

I also asked David Roberts on Google+, who answered

The overarching aim is to categorify certain aspects of John McKay’s work.

The specific aim is to show that certain finite groups are the group of isomorphism classes of certain 2-groups, or for the case of skeletal 2-groups or strict 2-groups, the group of objects. One of her students did this for the platonic groups (certain groups embeddable in Spin(3)~S 3Spin(3) ~ S^3), and this involved String(3)String(3).

One of the key techniques is to consider a categorification of the relationship between Lie groups, maximal tori and Weyl groups, so that one can relate the Lie side of things and the discrete side of things. Using the torus given by the Leech lattice she says she can push this programme up to Co 0Co_0 = Aut(Leech lattice).

Another point is that she (and collaborators) want to get the Monster 2-group as the autoequivalence 2-group of some reasonably natural object in a 2-category, and it looks like an Enhanced TFT (something like a stripped down CFT) will be such a thing. At any rate, something simpler than the Frenkel, Lepowsky, Meurman VOA (‘simpler’ in some sense). (looking around I find this which might interest you)

When I talked with her, I forgot to ask about the sporadics being ‘things which are accidentally groups’, I’ll bring it up again.

So it’s not there yet, but a clear programme to build towards it is well under way.

Posted by: David Corfield on July 18, 2013 8:24 AM | Permalink | Reply to this

Re: Category Theory 2013

One small correction: I should have said Ganter and Matt Ando are looking at getting the StringString as the autoequivalence 2-group of an Enhanced/Enriched TFT. There’s conjecturally something else of which the Monster 2-group will be the autoequivalence 2-group, but I don’t know if there’s any idea what it might be, yet.

Ganter also has as collaborators here her students Narthana Epa and Robert Usher.

Posted by: David Roberts on July 18, 2013 8:39 AM | Permalink | Reply to this

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