Are all 2-divisible Abelian groups natural? In 2-divisible groups, we can divide by 2. This is a big question and it appears to be a big cardinality problem. The video below explains this a bit. If one learns group theory one can have the impression that “abelian groups are boring”. …
Again a little bit of a flashback to my earliest steps in doing mathematical research. The Pentagonal number theorem is one of the most beautiful theorems in number theory. It uses the Pentagonal numbers to get a recursion for the partition function . This can be written as ( typo …
The pendulum equation can be solved explicitly using the Weierstrass elliptic function.
This is a bit of an update on the problem to find the limiting law in the Barycentric central limit theorem. (See some older slides.) The distribution has first experimentally been found in the PeKeNePaPeTe paper in 2012. I proved universality in 2015 using a modification of the Lidski theorem …
