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.

Click here for the Zoom link and to sign up for the mailing list.

Click here for a list of past and upcoming talks.

Click here for the CodEx YouTube channel.

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.

Continue reading Kopp’s Whisky Prize

Algebra, geometry, and combinatorics of subspace packings

Last week, the SIAM Conference on Applied Algebraic Geometry hosted a session on “Algebra, geometry, and combinatorics of subspace packings,” organized by Emily King and myself. Sadly, I wasn’t able to attend, but thankfully, most of the speakers gave me permission to post their slides on my blog. Here’s the lineup:

Emily KingAlgebra, Geometry, and Combinatorics of Subspace Packings

Romanos MalikiosisGroup frames, full spark, and other topics

John Jasper Equiangular tight frames from nonabelian groups

Gene KoppSIC-POVM existence and the Stark conjectures

Continue reading Algebra, geometry, and combinatorics of subspace packings

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

Continue reading Foundations of Data Science Boot Camp, V

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

Continue reading Foundations of Data Science Boot Camp, IV

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

Continue reading Foundations of Data Science Boot Camp, III

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

Continue reading Foundations of Data Science Boot Camp, II

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

Continue reading Foundations of Data Science Boot Camp

Recent Advances in Packing

Last week, I co-organized (with Joey Iverson and John Jasper) a special session on “Recent Advances in Packing” for the AMS Spring Central Sectional Meeting at the Ohio State University. All told, our session had 13 talks that covered various aspects of packing, such as sphere packing, packing points in projective space, applications to quantum physics, and connections with combinatorics. It was a great time! And after the talks, we learned how to throw axes!

What follows is the list of speakers and links to their slides. (I anticipate referencing these slides quite a bit in the near future.) Thanks to all who participated!

Continue reading Recent Advances in Packing

Tight Frames and Approximation 2018

I just returned from an amazing workshop in New Zealand organized by Shayne Waldron. The talks and activities were both phenomenal! Here’s a photo by Emily King that accurately conveys the juxtaposition:

28059469_10112541778108014_4963753337247640734_n

A few of the talks gave me a lot to think about, and I wanted to take a moment to record some of these ideas.

Continue reading Tight Frames and Approximation 2018