Author Archives: apgoucher

Royal Wedding and Polymath16

Congratulations to Meghan Markle and Prince Harry on what is undoubtedly the most energetic Royal Wedding! In other news, following on from Aubrey de Grey’s 5-chromatic unit-distance graph, there has been an effort to study the algebraic structure of the … Continue reading

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Assorted news

This last week has been very exciting. On Thursday, I gave a talk in absentia at the 13th Gathering for Gardner on the topic of artificial life (thanks go to Dave Greene and Tom Rokicki for playing the slides and … Continue reading

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Cubical Type Theory

Previously, we discussed Homotopy Type Theory, which is an alternative foundation of mathematics with several advantages over ZFC, mainly for computer-assisted proofs. It is based on Martin-Löf’s intuitionistic type theory, but with the idea that types are spaces, terms are … Continue reading

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Diamonds

Tim Hutton recently presented me with a marvellous 3D-printed-graphite set of triakis truncated tetrahedra. These have a natural interpretation as the Voronoi cells of a diamond: the shapes that would form if you gradually enlarged the atoms until they tessellate … Continue reading

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Happy Noethday

I’ve just realised, with only two minutes to go, that it’s the 136th birthday of the great mathematician Emmy Noether. Naturally, you are probably already aware of many of her contributions to mathematics and theoretical physics, including Noetherian rings and … Continue reading

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Serge Vlăduţ : Lattices with exponentially large kissing numbers

Originally posted on Combinatorics and more:
   (I thank Avi Wigderson for telling me about it.) Serge Vlăduţ just arxived a paper with examples of lattices in such that the kissing number is exponential in . The existence of such a…

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A rather satisfying winter

Over the last couple of months, I have been experimenting with the use of SAT solvers. This research recently came to fruition, with Tomas Rokicki and me announcing a new discovery with the intention of writing up the methodology in … Continue reading

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