Pensieve header: October 20: Some Hochschild Homology.

Today. Trees from triangulations, then some Hochschild homology, then whatever you may suggest, then EIWL 9-12, then, if time, Patterns.

Topics (in no particular order). Whatever you may suggest; whatever comes to my mind; the Fibonacci numbers; the Catalan numbers; the Jones polynomial; a more efficient Jones algorithm; a riddle on spheres; Khovanov homology; Γ-calculus; the Hopf fibration; Hilbert’s 13th problem; non-commutative Gaussian elimination; free Lie algebras; the Baker-Campbell-Hausdorff formula; wacky numbers; an order 4 torus; the Schwarz Lantern; knot colourings; the Temperley-Lieb pairing; the dodecahedral link; sound experiments; barycentric subdivisions; a Peano curve; braid closures and Vogel’s algorithm; the insolubility of the quintic; phase portraits; the Mandelbrot set; shadows of the Cantor aerogel; quilt plots; some image transformations; De Bruijn graphs; the Riemann series theorem; finite type invariants and the Willerton fish; the Towers of Hanoi; Hochschild homology of (some) coalgebras; convolutions and image improvements.

An Image Manipulation Challenge

The image at http://drorbn.net/bbs/show?shot=17-1750-171016-111042.jpg is pathetic. Can you improve it? Whatever you do, should also work well with all other images at http://drorbn.net/bbs/show.php?prefix=17-1750.

Trees from Triangulations

triang=ds[d[9,11],d[9,12],d[0,12],d[0,9],d[2,7],d[2,6],d[3,5],d[2,5],d[2,8],d[0,8],d[0,2]];

triang /. ds[ls___] -> Graphics[{ls}] /. d[i_,j_]:>Line[{i,j}] /. j_Integer:>{Cos[((2π j)/14)], Sin[((2π j)/14)]}

Last[d[0,13](Times@@triang)(∏_(j=0)^12)e[j,j+1,●] //. e[i_,j_,t1_]e[j_,k_,t2_]d[i_,k_] :> e[i,k,p[t1,t2]]] // TreeForm

Some Hochschild Homology