# Four announcements (new positions and new papers)

A 4-in-1 post:

1. New PhD program in Data Science at NYU: http://cds.nyu.edu/phd-program/
2. New Moore-Sloan Data Science Fellow Position at NYU CDS: http://cds.nyu.edu/nyu-moore-sloan-data-science-fellows/
3. New Results on the Resilience of the Littlewood-Offord Problem: https://arxiv.org/abs/1609.08136
4. New Results on Optimality/Sub-optimality of PCA under Spike random matrix models: https://arxiv.org/abs/1609.05573

# Luis Daniel Abreu proves the (complex version of) the Monotonicity of Singular Values Conjecture

The semester is under way and, as I announced here, I am teaching a new version of the Mathematics of Data Science course I taught last fall. As I go through the material, and the open problems, I will announce here in the blog progress that has been done on the open problems since I last gave the class.

I am very happy to announce that Luis Daniel Abreu posted a proof for the complex version of the Conjecture regarding the Monotonicity of the average Singular Value of a Gaussian Matrix (see the Conjecture here: https://afonsobandeira.wordpress.com/2013/11/01/a-conjecture-on-the-singular-values-of-a-gaussian-matrix/ , it is Open Problem 1.2 of last years version of the class: http://www.cims.nyu.edu/~bandeira/Fall2015.18.S096.html )

Luis Daniel Abreu was a mentor of mine back in my undergraduate times, and was my first co-author! The solution is available in the arxiv at: http://arxiv.org/abs/1606.00494

# Mathematics of Data Science course at NYU Courant

I am teaching a Mathematics of Data Science PhD level course at NYU Courant this Fall, I’ll be posting new Open Problems in this blog! See more info here.

# SDP for Community Detection with many communities

I am happy to announce that there is significant progress on Open Problem 9.2. of my notes, in this paper Bruce Hajek, Yihong Wu, and Jiaming Xu show that, indeed, for $k = \Omega(\log n)$ communities, the natural Semidefinite Program is suboptimal!

Congratulations to the three!

# Ten Lectures and Forty-Two Open Problems in the Mathematics of Data Science

The lecture notes for the course I gave this semester are now available here. Thanks to all the readers that gave me comments and feedback on the notes! I am sure the notes still contain many typos, if you find one, or have any general feedback, please let me know!