Complex Projective 4-Space

I’ve been spending some of my time recently developing a tool called FPSan in collaboration with Pawel Szczerbuk.

This is an atypical post, being chiefly about the history of a rather obscure computer that was built in 1960 out of repurposed PDP parts, but it needs to be written somewhere lest it be forgotten.

In the post on threelds, we investigated under what conditions the additive group of one field (the ‘inner field’) could be isomorphic to the multiplicative group of another field (the ‘outer field’).

A phoenix is an oscillator in Conway’s Life where every cell dies in every generation.

Soon after the previous post announcing the discovery of an aperiodic monotile by Smith, Myers, Kaplan, and Goodman-Strauss, the same authors published a second aperiodic monotile which has the property that all of the tiles are of the same orientation: r…

David Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss have discovered an aperiodic monotile: a polygon that tiles the plane by rotations and reflections, but cannot tile the plane periodically.

A couple of years ago I described a prime p which possesses various properties that renders it useful for computing number-theoretic transforms over the field .

I gave a half-hour talk on Tuesday about the project to search for optimal Boolean chains for all equivalence classes of 5-input 1-output and 4-input 2-output functions.

In the tensor rank paper we introduced a new family of axis-aligned n-dimensional polytopes, one for each positive integer n.

Robin Houston, Nathaniel Johnston, and I have established some new bounds on the tensor rank of the determinant over various fields.