I’ve just uploaded to the arXiv the paper “Decomposing a factorial into large factors“. This paper studies the quantity , defined as the largest quantity such that it is possible to factorize into factors , each of which is at least . The first few values of this sequence are (OEIS A034258). For instance, we […]

There has been some spectacular progress in geometric measure theory: Hong Wang and Joshua Zahl have just released a preprint that resolves the three-dimensional case of the infamous Kakeya set conjecture! This conjecture asserts that a Kakeya set – a subset of that contains a unit line segment in every direction, must have Minkowski and […]

I recently returned from the 2025 Annual Meeting of the “Localization of Waves” collaboration (supported by the Simons Foundation, with additional related support from the NSF), where I learned (from Svitlana Mayboroda, the director of the collaboration as well as one of the principal investigators) of a remarkable statistic: net electricity consumption by residential customers […]