Category Archives: 10 Lectures and 42 Open Problems

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

18.S096: Synchronization Problems and Alignment

The last set of Lecture notes for my course are now available here and are about Synchronization problems. They also include the last four open problems of the course. I will document the open problems here, while referring a much more detailed description of the problems on the notes, including description of partial progress.

Continue reading 18.S096: Synchronization Problems and Alignment

18.S096: Community dection and the Stochastic Block Model

A new set of lecture notes is available here about community detection and recovery in the stochastic block model, including five open problems . As usual, I will document the open problems here, while referring a much more detailed description of the problems on the notes, including description of partial progress.

Continue reading 18.S096: Community dection and the Stochastic Block Model

18.S096: Group Testing and Error-Correcting Codes

A new set of Lecture notes is available here. These ones are about group testing and contain a very brief “crash-course” on error-correction codes. They also include five open problems. As usual, I will document the open problems here, while referring a much more detailed description of the problems on the notes.

Continue reading 18.S096: Group Testing and Error-Correcting Codes