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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.

In 2010, the UCLA mathematics department launched a scholarship opportunity for entering freshman students with exceptional background and promise in mathematics. We are able to offer one scholarship each year. The UCLA Math Undergraduate Merit Scholarship provides for full tuition, and a room and board allowance for 4 years, contingent on continued high academic performance. In addition, scholarship recipients follow an individualized accelerated program of study, as determined after consultation with UCLA faculty. The program of study leads to a Masters degree in Mathematics in four years.

More information and an application form for the scholarship can be found on the web at:

http://www.math.ucla.edu/ugrad/mums

To be considered for Fall 2018, candidates must apply for the scholarship and also for admission to UCLA on or before November 30, 2017.

I just learned (from Emmanuel Kowalski’s blog) that the AMS has just started a repository of open-access mathematics lecture notes. There are only a few such sets of notes there at present, but hopefully it will grow in the future; I just submitted some old lecture notes of mine from an undergraduate linear algebra course I taught in 2002 (with some updating of format and fixing of various typos).

[Update, Dec 22: my own notes are now on the repository.]

[This guest post is authored by Caroline Series.]

The Chern Medal is a relatively new prize, awarded once every four years jointly by the IMU

and the Chern Medal Foundation (CMF) to an individual whose accomplishments warrant

the highest level of recognition for outstanding achievements in the field of mathematics.

Funded by the CMF, the Medalist receives a cash prize of US$ 250,000. In addition, each

Medalist may nominate one or more organizations to receive funding totalling US$ 250,000, for the support of research, education, or other outreach programs in the field of mathematics.

Professor Chern devoted his life to mathematics, both in active research and education, and in nurturing the field whenever the opportunity arose. He obtained fundamental results in all the major aspects of modern geometry and founded the area of global differential geometry. Chern exhibited keen aesthetic tastes in his selection of problems, and the breadth of his work deepened the connections of geometry with different areas of mathematics. He was also generous during his lifetime in his personal support of the field.

Nominations should be sent to the Prize Committee Chair: Caroline Series, email: chair@chern18.mathunion.org by 31st December 2016. Further details and nomination guidelines for this and the other IMU prizes can be found at http://www.mathunion.org/general/prizes/

Over the last few years, a large group of mathematicians have been developing an online database to systematically collect the known facts, numerical data, and algorithms concerning some of the most central types of objects in modern number theory, namely the L-functions associated to various number fields, curves, and modular forms, as well as further data about these modular forms. This of course includes the most famous examples of L-functions and modular forms respectively, namely the Riemann zeta function and the discriminant modular form , but there are countless other examples of both. The connections between these classes of objects lie at the heart of the Langlands programme.

As of today, the “L-functions and modular forms database” is now out of beta, and open to the public; at present the database is mostly geared towards specialists in computational number theory, but will hopefully develop into a more broadly useful resource as time develops. An article by John Cremona summarising the purpose of the database can be found here.

(Thanks to Andrew Sutherland and Kiran Kedlaya for the information.)

The International Mathematical Union (with the assistance of the Friends of the International Mathematical Union and The World Academy of Sciences, and supported by Ian Agol, Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Richard Taylor, and myself) has just launched the Graduate Breakout Fellowships, which will offer highly qualified students from developing countries a full scholarship to study for a PhD in mathematics at an institution that is also located in a developing country. Nominations for this fellowship (which should be from a sponsoring mathematician, preferably a mentor of the nominee) have just opened (with an application deadline of June 22); details on the nomination process and eligibility requirements can be found at this page.

Nominations for the 2017 Breakthrough Prize in mathematics and the New Horizons Prizes in mathematics are now open. In 2016, the Breakthrough Prize was awarded to Ian Agol. The New Horizons prizes are for breakthroughs given by junior mathematicians, usually restricted to within 10 years of PhD; the 2016 prizes were awarded to Andre Neves, Larry Guth, and Peter Scholze (declined).

The rules for the prizes are listed on this page, and nominations can be made at this page. (No self-nominations are allowed, for the obvious reasons; also, a third-party letter of recommendation is also required.)

Just a quick post to note that the arXiv overlay journal Discrete Analysis, managed by Timothy Gowers, has now gone live with its permanent (and quite modern looking) web site, which is run using the Scholastica platform, as well as the first half-dozen or so accepted papers (including one of my own). See Tim’s announcement for more details. I am one of the editors of this journal (and am already handling a few submissions). Needless to say, we are happy to take in more submissions (though they will have to be peer reviewed if they are to be accepted, of course).

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