Announcing a short course in Paris

This coming academic year I am on sabbatical, in Paris. It’s certainly a funny year to be on sabbatical. (It’s a funny year to be doing anything, isn’t it? Or is “funny” not the appropriate word…Yet I can’t find any other way to look at it that doesn’t send me straight into the abyss. So, let it be “funny”—knowing that, no, I’m not actually laughing right now.) On the one hand, I am lucky to have escaped the incessant debates on the format of teaching, how many people per square foot are allowed in each building on campus, what distance I should stay from my students were I to attempt to meet them in person, and so many other similar decisions that have come to take up a larger and larger fraction of our professional lives (not to mention of course the incommensurate challenges that many are facing at the personal and familial level). On the other hand, the situation makes it much harder to meet others and engage in new collaborations, one of the goals of my sabbatical. I’ll see how it plays out; I’ll be sure to write more on this blog as time progresses.

During the sabbatical I am being hosted successively by different French institutions. For the first 6 months I had the good fortune of being awarded a “chair” from the “Fondation Sciences Mathématiques de Paris” (FSMP), a private foundation which supports, in very general terms, the development of the mathematics community in Paris, from the organization of general-public conferences to the support of research collaborations. My only formal obligation during these 6 months is to give 20 hours of lecture on a theme of my choosing. The goal that I elected for the course is provide an in-depth introduction to two major works in quantum complexity and cryptography of the past few years: first, Mahavev’s 2018 result on classical verification of quantum computation (a result for which I already shared my enthusiasm here); second, my result MIP*=RE with Ji, Natarajan, Wright and Yuen on the power of quantum multi-prover interactive proof systems, which I mentioned in the previous post, and its consequences. For more about the course, including a tentative breakdown of lectures and some resources, see the course webpage.

While at the time of writing the course is still scheduled to start as an in-person meeting (to take place in a very large layered amphitheater with ample space for social distancing), there is no telling how the situation, and regulations, will evolve in the near future. To accommodate participants who are unable or prefer not to travel in person, all lectures starting with the first one will be recorded. In addition I will post course materials, including lecture notes, here. The purpose of this post is to advertise the course: participants from everywhere are welcome to watch the recorded videos, read the notes, and write to me with any questions in suggestions. In particular I plan to outsource the proof-reading of the notes via overleaf and I welcome any participant’s interest in helping with that; draft notes for the first lecture are already available here. Anyone is welcome to make direct corrections, or add inline comments pointing to issues that may need my attention.

The program that I chose is ambitious, and we will see how far we get along. My goal is to start slow, so as to remain inclusive with respect to varying backgrounds in computer science, mathematics or physics. At first I will give complete definitions, state and prove simple lemmas, etc., in order to establish common language. As time progresses I expect that things will become a little more high-level, less self-contained, and more technical. Depending on your background and interests, you may find the first few lectures, or the last few ones, more interesting. Teaching the course will certainly be beneficial for me because I believe that there is a strong unity behind the two works I chose to present. I hope to make that unity apparent by presenting them together. Moreover, both works introduce new techniques that leave many avenues open; I hope that a “clean” presentation will help me, and others, build on them.

A side benefit of an “un-necessary” course such as this one is that it contributes to bringing a certain community together. (By “un-necessary” I mean that the course will not be required for any curriculum; if it did not take place, as long as it was replaced by other research-level activities its absence would not be felt.) COIVD-19 unfortunately turns that opportunity into a challenge. It is because of it that I insist–regulations allowing– on having the course take place in person: as much as we are getting used to Zoom, and as well as it may be working as a replacement for many aspects of our interactive lives, from in-person classes to conferences to research collaborations, a scientific event such as this one, with sustained involvement by a small set of participants coming from distant backgrounds, is probably one of the more challenging ones to make work online. I hope it doesn’t come to that. Even if it does, one of the lessons learned from the Spring 2020 semester on quantum computing at the Simons Institute in Berkeley, which was interrupted half-ways due to the pandemic, is that having an initial in-person phase was of great help to cement future online interactions. So, I hope that I am able to lecture on Tuesday; after that, we will see.