Category Archives: Other Mathematical Topics

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!


Courant Institute of Mathematical Sciences

Finally, I am no longer in the job market! I am excited to announce that I will join the Courant Institute of Mathematical Sciences as an Assistant Professor in the Department of Mathematics with a joint appointment in the Center for Data Science!

I will join Courant in the Summer of 2016, until then I am spending a year in the Department of Mathematics at MIT as an Instructor of Applied Mathematics.

Warm thanks to all the other departments that hosted me this Spring and all of the people that helped me enjoy each and every visit, rendering my final decision extremely difficult! I had an amazing time, albeit completely exhausting.

The 4M-4 conjecture is false!

Cynthia Vinzant just disproved part (a) of the {4M-4} conjecture, see here!

We posed the {4M-4} conjecture two years ago, and there was even a monetary motivation for it! I will not go into details regarding the conjecture, you can read more about it either on a previous blog post of mine or a post of Dustin Mixon. In a nutshell it tries to predict how many phaseless measurements are needed to identify a complex vector of M dimensions. The conjecture was that (a) {4M-4} measurements are always needed and (b) {4M-4} measurements suffice (as long as sufficiently generic).

Continue reading The 4M-4 conjecture is false!