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.

**Open Problem 10.1. (Angular Synchronization via Projected Power Method)**

Does the projected power method converge (with high probability) to the optimal solution of the angular synchronization problem with (small enough) gaussian noise?

**Open Problem 10.2. (Sharp tightness of the Angular Synchronization SDP)**

Is the SDP for angular synchronization tight (with high probability) for noise levels essentially until the solution of angular synchronization no longer correlates with the ground truth?

**Open Problem 10.3. (Tightness of the Multireference Alignment SDP)**

For which levels of noise is the SDP for Multireference Alignment tight?

**Open Problem 10.4. (Consistency and sample complexity of Multireference Alignment)**

- Is the Maximum likelihood for Multireference Alignment consistent? (after fixing the power spectrum)
- What is the sample complexity of the Multireference Alignment problem?

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