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Just a short post to announce that nominations are now open for the Maryam Mirzakhani New Frontiers Prize, which is a newly announced annual $50,000 award from the Breakthrough Prize Foundation presented to early-career, women mathematicians who have completed their PhDs within the past two years, and recognizes outstanding research achievement. (I will be serving on the prize committee.) Nominations for this (and other breakthrough prizes) can be made at this page.

In the fall quarter (starting Sep 27) I will be teaching a graduate course on analytic prime number theory. This will be similar to a graduate course I taught in 2015, and in particular will reuse several of the lecture notes from that course, though it will also incorporate some new material (and omit some material covered in the previous course, to compensate). I anticipate covering the following topics:

- Elementary multiplicative number theory
- Complex-analytic multiplicative number theory
- The entropy decrement argument
- Bounds for exponential sums
- Zero density theorems
- Halasz’s theorem and the Matomaki-Radziwill theorem
- The circle method
- (If time permits) Chowla’s conjecture and the Erdos discrepancy problem

Lecture notes for topics 3, 6, and 8 will be forthcoming.

The AMS and MAA have recently published (and made available online) a collection of essays entitled “Living Proof: Stories of Resilience Along the Mathematical Journey”. Each author contributes a story of how they encountered some internal or external difficulty in advancing their mathematical career, and how they were able to deal with such difficulties. I myself have contributed one of these essays; I was initially somewhat surprised when I was approached for a contribution, as my career trajectory has been somewhat of an outlier, and I have been very fortunate to not experience to the same extent many of the obstacles that other contributors write about in this text. Nevertheless there was a turning point in my career that I write about here during my graduate years, when I found that the improvised and poorly disciplined study habits that were able to get me into graduate school due to an over-reliance on raw mathematical ability were completely inadequate to handle the graduate qualifying exam. With a combination of an astute advisor and some sheer luck, I was able to pass the exam and finally develop a more sustainable approach to learning and doing mathematics, but it could easily have gone quite differently. (My ~~20~~ 25-year old writeup of this examination, complete with spelling errors, may be found here.)

Just a short note to point out that submissions to the 2019 Breakthrough Junior Challenge are now open until June 15. Students ages 13 to 18 from countries across the globe are invited to create and submit original videos (3:00 minutes in length maximum) that bring to life a concept or theory in the life sciences, physics or mathematics. The submissions are judged on the student’s ability to communicate complex scientific ideas in engaging, illuminating, and imaginative ways. The Challenge is organized by the Breakthrough Prize Foundation, in partnership with Khan Academy, National Geographic, and Cold Spring Harbor Laboratory. The winner of the challenge recieves a $250K college scholarship, with an addition $50K prize to the winner’s maths or science teacher, and a $100K lab for the student’s school. (This year I will be on the selection committee for this challenge.)

Just a brief announcement that the AMS is now accepting (until June 30) nominations for the 2020 Joseph L. Doob Prize, which recognizes a single, relatively recent, outstanding research book that makes a seminal contribution to the research literature, reflects the highest standards of research exposition, and promises to have a deep and long-term impact in its area. The book must have been published within the six calendar years preceding the year in which it is nominated. Books may be nominated by members of the Society, by members of the selection committee, by members of AMS editorial committees, or by publishers. (I am currently on the committee for this prize.) A list of previous winners may be found here. The nomination procedure may be found at the bottom of this page.

Now that Google Plus is closing, the brief announcements that I used to post over there will now be migrated over to this blog. (Some people have suggested other platforms for this also, such as Twitter, but I think for now I can use my existing blog to accommodate these sorts of short posts.)

- The NSF-CBMS regional research conferences are now requesting proposals for the 2020 conference series. (I was the principal lecturer for one of these conferences back in 2005; it was a very intensive experience, but quite enjoyable, and I am quite pleased with the book that resulted from it.)
- The awardees for the Sloan Fellowships for 2019 have now been announced. (I was on the committee for the mathematics awards. For the usual reasons involving the confidentiality of letters of reference and other sensitive information, I will be unfortunately be unable to answer any specific questions about our committee deliberations.)

Just a quick post to advertise two upcoming events sponsored by institutions I am affiliated with:

- The 2019 National Math Festival will be held in Washington D.C. on May 4 (together with some satellite events at other US cities). This festival will have numerous games, events, films, and other activities, which are all free and open to the public. (I am on the board of trustees of MSRI, which is one of the sponsors of the festival.)
- The Institute for Pure and Applied Mathematics (IPAM) is now accepting applications for its second Industrial Short Course for May 16-17 2019, with the topic of “Deep Learning and the Latest AI Algorithms“. (I serve on the Scientific Advisory Board of this institute.) This is an intensive course (in particular requiring active participation) aimed at industrial mathematicians involving both the theory and practice of deep learning and neural networks, taught by Xavier Bresson. (Note: space is very limited, and there is also a registration fee of $2,000 for this course, which is expected to be in high demand.)

Just a quick announcement that Dustin Mixon and Aubrey de Grey have just launched the Polymath16 project over at Dustin’s blog. The main goal of this project is to simplify the recent proof by Aubrey de Grey that the chromatic number of the unit distance graph of the plane is at least 5, thus making progress on the Hadwiger-Nelson problem. The current proof is computer assisted (in particular it requires one to control the possible 4-colorings of a certain graph with over a thousand vertices), but one of the aims of the project is to reduce the amount of computer assistance needed to verify the proof; already a number of such reductions have been found. See also this blog post where the polymath project was proposed, as well as the wiki page for the project. Non-technical discussion of the project will continue at the proposal blog post.

Next quarter (starting Monday, April 2) I will be teaching Math 246C (complex analysis) here at UCLA. This is the third in a three-series graduate course on complex analysis; a few years ago I taught the first course in this series (246A), so this course can be thought of in some sense as a sequel to that one (and would certainly assume knowledge of the material in that course as a prerequisite), although it also assumes knowledge of material from the second course 246B (which covers such topics as Weierstrass factorization and the theory of harmonic functions).

246C is primarily a topics course, and tends to be a somewhat miscellaneous collection of complex analysis subjects that were not covered in the previous two installments of the series. The initial topics I have in mind to cover are

- Elliptic functions;
- The Riemann-Roch theorem;
- Circle packings;
- The Bieberbach conjecture (proven by de Branges); and
- the Schramm-Loewner equation (SLE).
- This list is however subject to change (it is the first time I will have taught on any of these topics, and I am not yet certain on the most logical way to arrange them; also I am not completely certain that I will be able to cover all the above topics in ten weeks). I welcome reference recommendations and other suggestions from readers who have taught on one or more of these topics.

As usual, I will be posting lecture notes on this blog as the course progresses.

[Update: Mar 13: removed elliptic functions, as I have just learned that this was already covered in the prior 246B course.]

Alice Guionnet, Assaf Naor, Gilles Pisier, Sorin Popa, Dimitri Shylakhtenko, and I are organising a three month program here at the Institute for Pure and Applied Mathematics (IPAM) on the topic of Quantitative Linear Algebra. The purpose of this program is to bring together mathematicians and computer scientists (both junior and senior) working in various quantitative aspects of linear operators, particularly in large finite dimension. Such aspects include, but are not restricted to discrepancy theory, spectral graph theory, random matrices, geometric group theory, ergodic theory, von Neumann algebras, as well as specific research directions such as the Kadison-Singer problem, the Connes embedding conjecture and the Grothendieck inequality. There will be several workshops and tutorials during the program (for instance I will be giving a series of introductory lectures on random matrix theory).

While we already have several confirmed participants, we are still accepting applications for this program until Dec 4; details of the application process may be found at this page.

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