How do you count rooted planar n -ary trees with some number of leaves? For n = 2 this puzzle leads to the Catalan numbers. These are so fascinating that the combinatorist Richard Stanley wrote a ...

Following SoTFom II, which managed to feature three talks on Homotopy Type Theory, there is now a call for papers announced for SoTFoM III and The Hyperuniverse Programme, to be held in Vienna, ...

How do you count rooted planar n -ary trees with some number of leaves? For n = 2 this puzzle leads to the Catalan numbers. These are so fascinating that the combinatorist Richard Stanley wrote a ...

This week in our seminar on Cohomology and Computation we continued discussing the bar construction, and drew some pictures of a classic example: Week 26 (May 31) - The bar construction, continued.

When we’ve got a discrete topological group G — or in other words, just a plain old group — we usually call the classifying space of G an Eilenberg–Mac Lane space K (G, 1). This may alternatively be ...

The math-blogosphere is abuzz with interest in the new Math Overflow, a mathematics questions and answers site. Already we at the Café have been helped with the answer to a query on the Fourier ...

Update 21 May 2004 I have found out by now that what I was trying to argue here has already been found long ago in papers on background independence of string field theory. For instance on p.2 of ...

A while back Gina asked why computer scientists should be interested in categories. Maybe you categorical computer scientists out there have your own favorite answers to this? I’d be glad to hear them ...

Finally we get to see James Dolan in action, talking about Geometric Representation Theory! While I’ve been focusing on examples, now we’ll start to see the general principles at work in geometric ...

We should probably focus on the mathematicians who aren’t already blogging and perhaps don’t know much about it — since the ones who do, don’t need to read the Notices to learn about the issues. What ...

In the penultimate lecture of last fall’s Geometric Representation Theory seminar, James Dolan lays the last pieces of groundwork for the Fundamental Theorem of Hecke Operators. I’ll actually state ...

where on the far right we have the very large (∞, 1) -topos on pro-objects in C, and where (∞, 1) Topos C is supposed to denote here the C -structured (∞, 1) -toposes – supposed to be the petit ones! ...