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Fact of the day: dice are chiral

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Fact of the day: Condorset domains, tiling permutations and contractibility


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 are the Minkowski sums \( \Z(k,l)=s_k\oplus s_l, 1\leq k\lt l\leq n\) of pairs of the segments. Tilings of \( \Z\) by \( n\choose 2\) rhombuses \( \Z(k,l)\) define also an oriented graph (formed by the edges of the rhombuses, and oriented up in the plane).…

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coming soon.…

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Topologically constrained models of statistical physics.


The Blob

Consider the following planar “spin model”: the state of the system is a function from \(\Int^2\) into \(\{0,1\}\) (on and off states). We interpret the site \((i,j), i,j\in\Int\) as the plaque, i.e. the (closed) square given by the inequalities \(s_{ij}:=i-1/2\leq x\leq i+1/2; j-1/2\leq y\leq j+1/2\).

To any configuration \(\eta\) we associate the corresponding active domain,
A_\eta=\bigcup_{(i,j): \eta(i,j)=1} s_{ij}.

We are interested in the statistical ensembles supported by the finite contractible active domains – let’s refer to such domains as blobs.…

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Topology in Motion @ICERM Fall’16

If you are interested in Applied Topology, tend to plan far, far ahead and have some free time on your hands in Fall 2016, check this out, and let us know!


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more on humanitarian disaster

Bug in the system

Handling of all – not just Salaita’s – cases by U of I is deficient, with the final approval coming only after the move to campus is done. We all are culpable, registering this issue when hired, then happily forgetting about it, waiting for that ticking bomb to explode, relying on assumptions. Debugging this procedure should be done as soon as possible. It seems the administration acts on it.

Role of Trustees

in terms of procedure they were fully within their prerogative not confirming Salaita’s appointment, as

the Board of Trustees exercises final authority over the University.

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arrieregarde battles of postmodernism

The epicenter of the battle around Salaita’s offer withdrawal seems to be located at the question, whether or not political considerations are admissible when appointing a scholar. I checked what Dr. Salaita himself writes about the matter in a 2008 paper dealing specifically with academic freedom.

A general remark on the paper: most of it consists of unsolicited, unadulterated punditry, bloated with (intentionally, I guess) opaque and (sometimes comically) elevated prose, mainly arguing with a group of Internet writers expressing their views too noisily and/or too effectively, to author’s taste.…

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hyperbolic geometry of Google maps


Google Maps and the Space of Views

Let’s consider the geometry hidden behind one of the best user interfaces in mobile apps ever, – the smartphone maps, the ones which you can swipe, flick and pinch. We are not talking here about the incredible engine that generates the maps on the fly as your finger waddles over the screen – just about the interface, which in a very intuitive and remarkably efficient way allows you to move between various maps.…

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This summer Yura Mileyko and I gave a tutorial on Topological Data Analysis at ISIT 2014. It was intended as a gentle introduction aimed at people who never heard about homologies (outside of, say, biology) – and there were plenty of those in the audience!

The result is idiosyncratic and lopsided – here are the slides……

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Voice of Russia puts Urbana on the war map (never mind the grammar or arithmetic)


“A new wave of a massive D-Dos attack hit our site at 1 o’clock pm last night,” the organizers of the Crimean referendum have just reported.
“Our IT safety experts managed to find out where those attacks came from. It is University of Illinois at Urbana Champaign. The most powerful scanning of servers before the attack was carried out exactly from there.”
It is significant that Urbana – Champaign, with a population of 37,000, has the highest number of subnets with IP addresses.

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