Explore: mathematics

Tensor rank paper | Complex Projective 4-Space (cp4space.hatsya.com)
Robin Houston, Nathaniel Johnston, and I have established some new bounds on the tensor rank of the determinant over various fields. The paper is now available as an arXiv preprint and contains the following results: A new formula for the determinant (Houston's identity) which applies over arbitrary commutative rings and establishes an upper bound of...
Mathgen Books (thatsmathematics.com)
diversions, distractions, and math
Algebraic Probability - Almost Sure (almostsuremath.com)
The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists...