## December 31, 2008

### Joint Math Meetings in Washington DC

#### Posted by John Baez

In just a few days, hordes of mathematicians will descend on Washington DC for the big annual joint meeting of the American Mathematical Society (AMS), Mathematical Association of America (MAA), Society for Industrial and Applied Mathematics (SIAM), and sundry other societies, organizations, clubs, conspiracies and cabals:

I’ll be there. Will you?

I’m giving two talks — you can see the slides here.

The first is at the special session on Homotopy Theory and Higher Categories, run by Tom Fiore, Mark Johnson, Jim Turner, Steve Wilson and Donald Yau. When I last checked, it was scheduled for Wednesday January 7th, 1–1:20 pm in Virginia Suite C, Lobby Level in the Marriott:

• Classifying Spaces for Topological 2-Groups — joint work with Danny Stevenson.

Abstract: Categorifying the concept of topological group, one obtains the notion of a topological 2-group. This in turn allows a theory of ‘principal 2-bundles’ generalizing the usual theory of principal bundles. It is well-known that under mild conditions on a topological group $G$ and a space $M$, principal $G$-bundles over $M$ are classified by either the Cech cohomology $H^1(M,G)$ or the set of homotopy classes $[M,B G]$, where $B G$ is the classifying space of $G$. Here we review work by Bartels, Jurco, Baas-Bökstedt-Kro, Stevenson and myself generalizing this result to topological 2-groups. We explain various viewpoints on topological 2-groups and the Cech cohomology $H^1(M,\mathbf{G})$ with coefficients in a topological 2-group $\mathbf{G}$, also known as ‘nonabelian cohomology’. Then we sketch a proof that under mild conditions on $M$ and $\mathbf{G}$ there is a bijection between $H^1(M,\mathbf{G})$ and $[M,B|N\mathbf{G}|]$, where $B|N\mathbf{G}|]$ is the classifying space of the geometric realization of the nerve of $\mathbf{G}$.
Here are some talks by friends of mine at the same session:
• Peter May, Permutative and bipermutative categories revisited.
• Mike Shulman, Limits, derived functors, and homotopical category theory.
• Julie Bergner, Homotopical versions of Hall algebras.
• Tom Fiore, The homotopy theory of n-fold categories.

I’ll also give talk at the special session on Categorification and Link Homology, run by Aaron Lauda and Mikhail Khovanov. When I last checked, it was scheduled for Wednesday January 7th, 5:10 - 5:30 pm, in the Harding Room, Mezzanine Level, Marriott:

• Groupoidification — joint work with James Dolan, Todd Trimble, Alex Hoffnung and Christopher Walker.

Abstract: There is a systematic process that turns groupoids into vector spaces and spans of groupoids into linear operators. ‘Groupoidification’ is the attempt to reverse this process, taking familiar structures from linear algebra and enhancing them to obtain structures involving groupoids. Like quantization, groupoidification is not entirely systematic. However, examples show that it is a good thing to try! For example, groupoidifying the quantum harmonic oscillator yields combinatorial structures associated to the groupoid of finite sets, while groupoidifying the $q$-deformed oscillator yields structures associated to finite-dimensional vector spaces over the field with $q$ elements. Starting with flag varieties defined over the field with $q$ elements, we can also groupoidify Hecke and Hall algebras.

Here are some talks by friends and fellow math bloggers at the same session:

• Scott Morrison, The 2-point and 4-point Khovanov categories.
• Ben Webster, A categorification of quantum tangle invariants via quiver varieties.
• Hendryk Pfeiffer, Every modular category is the category of modules over an algebra.
• Alex Hoffnung, A categorification of Hecke algebras.

Alex’s talk will pick up where mine leaves off.

My student Alissa Crans will also be there; she and Sam Nelson are running the special session on Algebraic Structures in Knot Theory. Charles Frohman and Louis Kauffman will be talking at that — I used to see them fairly often, back when I was into knots and quantum gravity.

During the conference I’ll stay with my friend the combinatorialist Bill Schmitt, who lives in Bethesda, conveniently located next to the subway into DC. We went to grad school at MIT together. He’s a student of Rota, and he’s the one who got me interested in Joyal’s work on ‘species’.

Given this profusion of friends attending the conference, I expect there’ll be some serious socializing going on. Mathematically speaking, that’s actually more productive than the ridiculously short 20-minute talks. And, it’s more fun. I really like it when two people I know and admire, who haven’t ever met, finally meet. There’ll be a lot of that going on here.

Who else reading this will be there?

Posted at December 31, 2008 2:38 AM UTC

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### Re: Joint Math Meetings in Washington DC

I’ll be there. A convenient farewell tour.

Posted by: John Armstrong on December 31, 2008 4:04 AM | Permalink | Reply to this

### Re: Joint Math Meetings in Washington DC

Farewell tour? This sounds ominous!

Posted by: Mikael Vejdemo Johansson on January 1, 2009 1:24 PM | Permalink | Reply to this

### Re: Joint Math Meetings in Washington DC

On the same day that your recent papers appear on the ArXiv, we have Raphael Rouquier writing on 2-Kac-Moody algebras:

We construct a 2-category associated with a Kac-Moody algebra and we study its 2-representations. This generalizes earlier work with Chuang for type $A$. We relate categorifications relying on $K_0$ properties and 2-representations.

At the end of the introduction he writes:

Certain specializations of the nil Hecke algebras associated with quivers and the resulting monoidal categories associated with “half” Kac-Moody algebras have been introduced independently by Khovanov and Lauda.

Posted by: David Corfield on December 31, 2008 12:31 PM | Permalink | Reply to this

### Re: Joint Math Meetings in Washington DC

Alas, I will miss the joint meetings. Happily, I will be at Knots in Washington. I think Masahico will be at the joint meetings and KinW.

Posted by: Scott Carter on December 31, 2008 5:31 PM | Permalink | Reply to this

### Re: Joint Math Meetings in Washington DC

As you know, Alissa Crans will be staying for Knots in Washington. Alex Hoffnung, Aaron Lauda, Louis Kauffman and Mikhail Khovanov will also be staying for that. My friend Bill Schmitt teaches at George Washington University, where this conference is being held, so you may also bump into him — try!

I can’t stay for that conference. Some of us need to teach!

Posted by: John Baez on December 31, 2008 7:22 PM | Permalink | Reply to this

### Re: Joint Math Meetings in Washington DC

I’ll be there! AND I’ll really, really, REALLY want to meet all the bloggers I regularly interact with!

Posted by: Mikael Vejdemo Johansson on January 1, 2009 1:25 PM | Permalink | Reply to this

### Re: Joint Math Meetings in Washington DC

Which sessions will you be going to? On Wednesday I’ll be at Homotopy Theory and Higher Categories and Categorification and Link Homology. I don’t yet know what I’ll be doing the other days. Where might I bump into you?

Do you look like this? Are you always on the phone?

Posted by: John Baez on January 1, 2009 5:49 PM | Permalink | Reply to this

### Re: Joint Math Meetings in Washington DC

I haven’t yet looked through the schedule in detail - but one place I’ll be guaranteed to be is the Topological Methods in Applied Mathematics - since that’s why my trip gets paid. :-)

I’ll make sure I’ll put highlights up on http://blog.mikael.johanssons.org once I’ve dug through the program.

I do look like that - though not always with a cellphone glued to my ear, and not always dressed in my wedding frockcoat. :-) It’s probable that I’ll be wearing t-shirts, possibly with a Stanford long-sleeved t-shirt or sweater over it, for most if not all of the meeting.

Posted by: Mikael Vejdemo Johansson on January 2, 2009 10:07 AM | Permalink | Reply to this

### Re: Joint Math Meetings in Washington DC

I’m trying to decide which talks to attend on Monday. Here are two interesting ones at the same time:

Posted by: John Baez on January 2, 2009 9:19 PM | Permalink | Reply to this

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