In this episode, Grant Sanderson (GS) interviews Alex Kantorovich (AK) about all things academia, and what follows is some commentary by John Jasper (JJ), Hans Parshall (HP), and me (DM). Feel free to discuss further in the comments.
This post concludes the Polymath16 project. Of course, we anticipate that folks will continue to make progress on this problem on their own. If you’d like to update the Polymath16 community about your progress, feel free to comment on this post.
I asked Aubrey to offer a few words to reflect on our project:
Last summer, I launched an online seminar with Joey Iverson, John Jasper, and Emily King on the theory and applications of harmonic analysis, combinatorics, and algebra. We meet on Tuesdays at 1pm (Eastern time).
What follows is a nice problem that was recently posed by Mario Krenn. Progress on this problem may lead to new insights in quantum physics (see this, this, this, and this for details). In addition, Mario has announced two cash prizes to encourage work in this direction. (!)
Consider a weighted and edge-colored bipartite graph consisting of
At the end of his recent CodEx talk, Gene Koppposed a problem with a prize attached to it. I was excited to learn about this, so I enlisted both Gene Kopp and Mark Magsino to help me write this blog entry to provide additional details.
First, let denote the set of matrices in such that
Here, denotes conjugate transpose, denotes entrywise squared modulus, denotes the identity matrix, and denotes the all-ones matrix. In words, the columns of form an equiangular tight frame (ETF) for of size .
The paper writing has found a second wind between Philip Gibbs, Aubrey de Grey, Jaan Parts and Tom Sirgedas. For reference, I wanted to compile a list of related publications that have emerged since starting our project. (Feel free to any references I missed in the comments.) There has certainly been a bit of activity since Aubrey’s paper first hit the arXiv two years ago!
At this point, much of the effort is transitioning to the writing stage, which is taking place on Overleaf. See this comment to obtain writing privileges for the paper. This thread can be used to discuss the write-up as well as any remaining research items.