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Several years ago, I developed a public lecture on the cosmic distance ladder in astronomy from a historical perspective (and emphasising the role of mathematics in building the ladder). I previously blogged about the lecture here; the most recent version of the slides can be found here. Recently, I have begun working with Tanya Klowden (a long time friend with a background in popular writing on a variety of topics, including astronomy) to expand the lecture into a popular science book, with the tentative format being non-technical chapters interspersed with some more mathematical sections to give some technical details. We are still in the middle of the writing process, but we have produced a sample chapter (which deals with what we call the “fourth rung” of the distance ladder – the distances and orbits of the planets – and how the work of Copernicus, Brahe, Kepler and others led to accurate measurements of these orbits, as well as Kepler’s famous laws of planetary motion). As always, any feedback on the chapter is welcome. (Due to various pandemic-related uncertainties, we do not have a definite target deadline for when the book will be completed, but presumably this will occur sometime in the next year.)

The book is currently under contract with Yale University Press. My coauthor Tanya Klowden can be reached at

My student, Jaume de Dios, has set up a web site to collect upcoming mathematics seminars from any institution that are open online.  (For instance, it has a talk that I will be giving in an hour.)   There is a form for adding further talks to the site; please feel free to contribute (or make other suggestions) in order to make the seminar list more useful.

UPDATE: Here are some other lists of mathematical seminars online:

Perhaps further links of this type could be added in the comments.  It would perhaps make sense to somehow unify these lists into a single one that can be updated through crowdsourcing.

EDIT: See also IPAM’s advice page on running virtual seminars.

The National Academies of Sciences, Engineering, and Medicine have initiated a project on “Illustrating the Impact of the Mathematical Sciences“, in which various media will be produced to showcase how mathematics impacts the modern world.  (I am serving on the committee for creating this media, which has been an interesting experience; the first time for instance that I have had to seriously interact with graphic designers.)  One of the first products is a “webinar” series on the ten topics our committee have chosen to focus on, that is currently running weekly on Tuesdays.  Last week I moderated the first such webinar, titled “From Solving to Seeing”, in which Profs. Gunther Uhlmann and Anna Gilbert presented ways in which inverse problems, compressed sensing, and other modern mathematical techniques have been used to obtain images (such as MRI images) that would not otherwise be accessible.  Next week I will moderate another webinar, titled “Abstract Geometry, Concrete Impact”, in which Profs. Katherine Stange and Jordan Ellenberg will discuss how modern abstract geometries are used in modern applications such as cryptography.  The full list of webinars and the latest information on the speakers can be found at this website.  (Past webinars can be viewed directly from the web site; live webinars require a (free) registration, and offer the ability to submit text questions to the speakers via the moderator.)

We are currently in the process of designing posters (and possibly even a more interactive online resource) for each of the ten topics listed in the webinars; hopefully these will be available in a few months.

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:

  1. Elementary multiplicative number theory
  2. Complex-analytic multiplicative number theory
  3. The entropy decrement argument
  4. Bounds for exponential sums
  5. Zero density theorems
  6. Halasz’s theorem and the Matomaki-Radziwill theorem
  7. The circle method
  8. (If time permits) Chowla’s conjecture and the Erdos discrepancy problem [Update: I did not end up writing notes on this topic.]

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.)

  1. 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.)
  2. 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:

  1. 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.)
  2. 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.)