Blog

Here I want to write about temporary interests, favorite open problems, neat arguments, random mathematical thoughts, things I want to remember, and stuff that is too little for a paper and too specific for Wikipedia.

Coned frameworks and radial moves

In my lecture today I proved that moving vertices radially in a coned framework preserves first-order rigidity. This is a precursor to a number of important results, such as…

Barycentric algebra

Today I hosted Anna Zamojska-Dzienio from the Warsaw University of Technology. She introduced me to barycentric algebras. Among other things, they allow us to see polytopes…

The Mahler conjecture for coordinate symmetric bodies

The Mahler conjecture asserts that among all centrally symmetric convex bodies \(B\) the cube minimizes the volume product \(\operatorname{vol}(B)\operatorname{vol}(B^\circ)\)…

The double kissing problem

Famously Isaac Newton and David Gregory disagreed over the maximal number of disjoint unit spheres that can simultaneously touch a central unit sphere. Newton claimed it to…