Note: These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older ...

Note: These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older ...

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 ...

Back to modal HoTT. If what was considered last time were all, one would wonder what the fuss was about. Now, there’s much that needs to be said about type dependency, types as propositions, sets, ...

Elementary Petri nets are the objects of a category N 𝒞 whose morphisms can represent simulations or refinements of them. The interpretations of the linear logic connectives of the dialectica ...

Why Mathematics is Boring I don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to ...

In this year’s edition of the Adjoint School we covered the paper Triangulations, orientals, and skew monoidal categories by Stephen Lack and Ross Street, in which the authors construct a concrete ...

Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional Distributional Model of Meaning, by Bob Coecke ...

I think I’m gradually coming to understand why some people think (∞, 1) -toposes are the best thing since sliced bread. For me, I think a brief way to describe what’s so amazing about them is that ...

For questions 1 and 2, isn’t that true for any group G, not just the fundamental groups of a manifold? And moreover, I think of this as the definition of the profinite completion of a group: as an ...

These are some lecture notes for a 4 1 2 -hour minicourse I’m teaching at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. To save time, I am ...

Trivial examples If μ ^ is the mean value of n uncorrelated individuals, then the effective sample size is n. If μ ^ is the mean value of n extremely highly correlated individuals, then the variance ...