2024年8月13日 · Guest post by Utku Boduroğlu, Drew McNeely, and Nico Wittrock When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful language to describe probability since the 17th century, and it works. Why change it up now? This may be a tempting question when ...

2024年12月4日 · TrackBack URL for this Entry: https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/3581

2024年8月15日 · I’m a little bemused by the popularity of the Galois theory notes. I’ve made quite a few sets of course notes public before, e.g.: Fourier analysis General topology Linear algebra Category theory But the Galois theory notes seem to have caught on in a way that none of the others have (except category theory — but that one, I made into a book). It’s true that I …

2024年10月29日 · Thurston’s paper Shapes of polyhedra and triangulations of the sphere is really remarkable. I’m writing about it in my next column for the Notices of the American Mathematical Society. Here’s a draft — which is also a much more detailed version of an earlier blog post here. If you have suggestions or corrections, please let me know: I …

2025年1月22日 · 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 browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing ...

2024年10月26日 · In their paper on this subject, Engel and Smillie claim to count the triangulations of the 2-sphere with n n triangles where at most 6 triangles meet at each vertex. To be precise they claim to count the groupoid cardinality of the groupoid of such triangulations: some of these triangulations have symmetries, and a triangulation with N N symmetries contributes 1 / N 1/N to the groupoid ...

2 天之前 · Last time, I talked about the magnitude of a set-valued functor. Today, I’ll introduce the comagnitude of a set-valued functor. I don’t know how much there is to the comagnitude idea. Let’s see! I’ll tell you all the interesting things I know about it. Along the way, I’ll also ask an ...

2024年10月31日 · Important dates Application opens: November 1, 2024 Application deadline: December 1, 2024 School runs: January-May, 2025 Research week dates: May 26-30, 2025 Who should apply? Anyone, from anywhere in the world, who is interested in applying category-theoretic methods to problems outside of pure mathematics. This is emphatically not restricted to math students, but one should be comfortable ...

2024年7月20日 · Foreword Once there was a thing called Twitter, where people exchanged short messages called ‘tweets’. While it had its flaws, I came to like it and eventually decided to teach a short course on entropy in the form of tweets. This little book is a slightly expanded version of that course. It’s easy to wax poetic about entropy, but what is …

We integrate this formula over moduli space Mg;n(L1;:::;Ln) using Mirzakhani’s integration formula which gives us an integral in terms of volumes of moduli spaces of surfaces with smaller j j: Z L1 vol(Mg;n(L1;:::;Ln)) = f(L;jxj)Vg;n( ;x; ;L) x dx: Rk+ Although the integrand is explicit, it is difficult to integrate. Instead we differentiate with respect to L1, integrate w.r.t. x 2 Rk ...