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).

Part (b) had been solved (positively) around a year ago Aldo Conca, Dan Edidin, Milena Hering, and Cynthia Vinzant (see the paper here) and part (a) was just disproved by Cynthia with an example in four dimensions.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s