## Codes and Expansions (CodEx) Seminar

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).

We’re kicking off the spring semester on January 26 with a talk from Steve Flammia on recent progress on Zauner’s conjecture.

## Kopp’s Whisky Prize

At the end of his recent CodEx talk, Gene Kopp posed 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 $\mathrm{ETF}(d,n)$ denote the set of matrices $A$ in $\mathbb{C}^{d\times n}$ such that

$\displaystyle|A^*A|^{2}=I_n+\frac{n-d}{d(n-1)}(J_n-I_n), \qquad AA^*=\frac{n}{d}I_d.$

Here, $*$ denotes conjugate transpose, $|\cdot|^2$ denotes entrywise squared modulus, $I_k$ denotes the $k\times k$ identity matrix, and $J_k$ denotes the $k\times k$ all-ones matrix. In words, the columns of $A$ form an equiangular tight frame (ETF) for $\mathbb{C}^d$ of size $n$.

## Foundations of Data Science Boot Camp, V

This is the fifth (and final) entry to summarize talks in the “boot camp” week of the program on Foundations of Data Science at the Simons Institute for the Theory of Computing, continuing this post. On Friday, we heard talks from Ilya Razenshteyn and Michael Kapralov. Below, I link videos and provide brief summaries of their talks.

Ilya Razenshteyn — Nearest Neighbor Methods

## Foundations of Data Science Boot Camp, IV

This is the fourth entry to summarize talks in the “boot camp” week of the program on Foundations of Data Science at the Simons Institute for the Theory of Computing, continuing this post. On Thursday, we heard talks from Santosh Vempala and Ilias Diakonikolas. Below, I link videos and provide brief summaries of their talks.

Santosh Vempala — High Dimensional Geometry and Concentration

## Foundations of Data Science Boot Camp, III

This is the third entry to summarize talks in the “boot camp” week of the program on Foundations of Data Science at the Simons Institute for the Theory of Computing, continuing this post. On Wednesday, we heard talks from Fred Roosta and Will Fithian. Below, I link videos and provide brief summaries of their talks.

Fred Roosta — Stochastic Second-Order Optimization Methods

## Foundations of Data Science Boot Camp, II

This is the second entry to summarize talks in the “boot camp” week of the program on Foundations of Data Science at the Simons Institute for the Theory of Computing, continuing this post. On Tuesday, we heard talks from Ken Clarkson, Rachel Ward, and Michael Mahoney. Below, I link videos and provide brief summaries of their talks.

Ken Clarkson — Sketching for Linear Algebra: Randomized Hadamard, Kernel Methods

## Foundations of Data Science Boot Camp

I’m spending the semester at the Simons Institute for the Theory of Computing as part of the program on Foundations of Data Science. This was the first day of the “boot camp” week, which was organized to acquaint program participants with the key themes of the program. Today, we heard talks from Ravi Kannan and David Woodruff. Below, I link videos and provide brief summaries of their talks.

Ravi Kannan — Foundations of Data Science