### Homotopy Theory and Higher Algebraic Structures at UC Riverside

#### Posted by John Baez

This year the Fall Western Section Meeting of the American Mathematical Society will be held here at UC Riverside. Julie Bergner and I are running a session on homotopy theory, $n$-categories and related topics. If you’re anywhere nearby, I hope you drop by!

- Special session on homotopy theory and higher algebraic structures, UC Riverside, November 7-8, 2009. Organized by Julie Bergner and John Baez.

If you’re interested in our session, you may also like this one:

- Special session on algebraic structures in knot theory, UC Riverside, November 7-8, 2009. Organized by Alissa Crans and Sam Nelson.

It’ll include talks by Louis Kauffman, Mikhail Khovanov, Scott Carter, Masahico Saito, Scott Morrison and other people who live near the interface of topology, categories and physics.

As if that weren’t enough, there’s also *another* session on knot theory:

- Special session on knotting around dimension three: a special session in memory of Xiao-Song Lin, UC Riverside, November 7-8, 2009. Organized by Martin Scharlemann and Mohammed Ait Nouh.

The special session that Julie Bergner and I put together has a great lineup of talks. First, here are the vaguely $n$-categorical talks, listed in no particular order:

Categorification via quiver varieties. Anthony Licata (with Sabin Cautis and Joel Kamnitzer). abstract.

Categorifying quantum groups. Aaron D Lauda. abstract.

2-Quandles: categorified quandles. Alissa S. Crans. abstract.

Group actions on categorified bundles. Weiwei Pan. abstract.

A categorification of Hall algebras. Christopher Walker. abstract.

A categorification of the Hecke algebra. Alexander E Hoffnung. abstract.

3-Categories for the working mathematician. Christopher L Douglas (with Andre Henriques). abstract.

Mapping spaces in quasi-categories. David I. Spivak (with Daniel Dugger). abstract.

String connections and supersymmetric sigma models. Konrad Waldorf. abstract.

As you can see, categorification is becoming a big business. Of course, a lot of this is due to the work of Mikhail Khovanov. And over in Alissa and Sam’s special session, he’s giving an hour-long talk entitled “Adventures in categorification”!

Second, here are the vaguely homotopy-theoretic talks. Of course there’s no sharp dividing line, and I’m not trying to create one… I’m just trying to avoid a single enormous list of talks which none of you will read:

Generating spaces for $S(n)$-acyclics. Aaron Leeman. abstract

A homotopy-theoretic view of Bott–Taubes integrals and knot spaces. Robin Koytcheff. abstract.

On the $K$-theory of toric varieties. Christian Haesemeyer (with Guillermo Cortinas, Mark E Walker, and Charles A. Weibel). abstract.

Homotopy colimits and the space of square-zero upper-triangular matrices. Jonathan W Lee. abstract.

An application of equivariant $\mathbb{A}^1$-homotopy theory to problems in commutative algebra. T Benedict Williams. abstract.

String topology and the based loop space. Eric J Malm. abstract.

Unstable Vassiliev theory. Chad D Giusti. abstract.

The Atiyah–Segal completion theorem in twisted $K$-theory. Anssi S. Lahtinen. abstract.

Monoids of moduli spaces of manifolds. Soren Galatius. abstract.

Relations amongst motivic Hopf elements. Daniel Dugger (with Daniel C. Isaksen). abstract.

Real Johnson-Wilson theories. Maia Averett. abstract.

Orbifolds and equivariant homotopy theory. Laura Scull (with Dorette Pronk). abstract.

Universal Bott Samelson resolutions. Nitu R Kitchloo. abstract.

There will also be a double talk on ‘blob homology’. I don’t completely understand blob homology yet, but it seems to be a practical way of computing homology with coefficients in an $n$-category with duals. If so, it straddles the worlds of $n$-category theory and homotopy theory so neatly that it makes a mockery of the distinction:

Blob homology 1. Scott Morrison (with Kevin Walker). abstract.

Blob Homology 2. Kevin Walker (with Scott Morrison) abstract.

If you want to know when the talks are actually taking places, check out the schedules here.

## Re: Homotopy Theory and Higher Algebraic Structures at UC Riverside

The basic idea of blob homology should be that of factorization algebra, which in turn is not unsimilar to local nets in AQFT.