A few years ago, I suggested to Daniel Feshbach at Cynthia Sung‘s lab to play with a curved origami design for a self-folding walking robot. He took off with that raw idea, and brought an extraordinary amount of engineering insight and ingenuity… (Here’s one of the first tries.) Now, the CurveQuad (I like to call …
2. Around Arrow published, – a riveting tale of cold war planning, trans-Atlantic rivalries, RAND corporation characters, lack of social networks in 1950-ies, and the ensuing non-emergence of applied topology half a century ago, – all there. No, really.
This visual continues the exploration started here. I used the dataset of MathSciNet records of the publications by department members, collected by the IGL participants. Each article reviewed by MSN carries a few MSC codes, roughly classifying them. I used these codes to create a sankey diagram, showing who published in what area. A few …
\(\def\Real{\mathbb{R}}\def\tree{\mathcal{T}}\) Consider a path metric space \(M\) and a continuous function \(f:M\to \Real\). For simplicity, all such pairs here will have sublevel sets of \(f\) compact (so that the function is bounded from below). Then one can form the so-called merge tree (see, e.g. here, for motivation, and some history), a new topological space (let’s …
\(\def\Real{\mathbb{R}}\def\Z{\mathcal{Z}}\def\sg{\mathfrak{S}}\def\B{\mathbf{B}}\def\xx{\mathbf{x}}\def\ex{\mathbb{E}}\) Consider \(n\) points in Euclidean space, \(\xx={x_1,\ldots, x_n}, x_k\in \Real^d, n\leq d+1\). Generically, there is a unique sphere in the affine space spanned by those points, containing all of them. This centroid (which we will denote as \(o(x_1,\ldots,x_n)\)) lies at the intersection of the bisectors \(H_{kl}, 1\leq k\lt l\leq n\), hyperplanes of points equidistant …
\(\def\Real{\mathbb{R}}\def\Z{\mathcal{Z}}\def\sg{\mathfrak{S}}\def\B{\mathbf{B}}\) Consider a collection of vectors \(e_1,\ldots,e_n\) in the upper half-plane, such that \( e_k=(x_k,1)\) and \( x_1>x_2\gt \ldots \gt x_n\). Minkowski sum of the segments ( s_k:=[0,e_k]) is a zonotope ( \Z). Rhombus in this context is the Minkowski sums \( \Z(k,l)=s_k\oplus s_l, 1\leq k\lt l\leq n\) of a pair of the segments, perhaps …
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\(\def\Comp{\mathbb{C}}\def\Proj{\mathbb{P}}\def\Nat{\mathbb{N}}\) This workshop is about complex analytic techniques usable in applications from classical combinatorial problems to asymptotic representation theory and cluster algebras. The scope is approximately what is covered by Pemantle-Wilson(-Melczer) book. I plan to report on what is going on here (reporting is sporadic and idiosyncratic). Lectures are streamed. Day One (all times PDT): …
analytic combinatorics in several variables (aimath, san jose 4-9.4.2022) Read More »
