# 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.

# 18.S096: Compressed Sensing and Sparse Recovery

Another set of Lecture notes for my course, this time about Compressed Sensing and Sparse Recovery, is available here. As usual, I will document the open problems here, while referring to a much more detailed description of the problems on the notes, including description of partial progress.

# 18.S096: Max-Cut and Approximation Algorithms

The eight set of Lecture notes, now about Max Cut and Approximation Algorithms, is available here. They include five open problems, briefly documented here. Please see the notes for a lot more detail on the problems, relevant references and more.

# 18.S096: An extra Open Problem

I have just added an extra open problem (4.6.) to the fourth set of lecture notes. I am documenting it here.

# 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.

# 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.

# 18.S096: Johnson-Lindenstrauss Lemma and Gordon’s Theorem

The fifth set of Lecture notes for my course is available here. They are about dimension reduction, Johnson-Lindenstrauss Lemma and Gordon’s Escape Through a Mesh Theorem, it also includes three 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.

# 18.S096: Concentration Inequalities, Scalar and Matrix Versions

The fourth set of Lecture notes for my course is available here. This one is large deviation and concentration inequalities, for sums of independent scalar or matrices random variables. It also has 5 open problems related to problems involving concentration of certain random matrices. 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.

# 18.S096: Spectral Clustering and Cheeger’s Inequality

A new set of Lecture notes for my course is available here. This one is about spectral clustering and Cheeger’s Inequality. In a nutshell spectral clustering can be seen as attempting to cluster a graph by clustering the corresponding points of its Diffusion Maps embedding and Cheeger’s Inequality provides a guarantee of performance (for the case of two clusters). Take a look!

As usual, I will document the open problems here. I remind that there is a much more detailed description of the problems on the notes, including description of partial progress.

# 18.S096: Graphs, Diffusion Maps, and Semi-supervised Learning

The second set of Lecture notes for my course is now available here.  This week’s notes are about graphs, embedding of graphs in Euclidean space (focusing in Diffusion Maps) and relations between behavior of a graph based semi-supervised learning method and Sobolev Embedding Theorem. Given the nature of these topics, these notes have a lot more images than normal, take a look!

The notes also describe three open problems that I would like to document here, there is a much more detailed description of the problems on the notes, including description of partial progress.