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About a year ago, I was contacted by Masterclass (a subscription-based online education company) on the possibility of producing a series of classes with the premise of explaining mathematical ways of thinking (such as reducing a complex problem to simpler sub-problems, abstracting out inessential aspects of a problem, or applying transforms or analogies to find new ways of thinking about a problem). After a lot of discussion and planning, as well as a film shoot over the summer, the series is now completed. As per their business model, the full lecture series is only available to subscribers of their platform, but the above link does contain a trailer and some sample content.

*[I am posting this advertisement in my capacity as chair of the Steering Committee for the UCLA Endowed Olga Radko Math Circle – T.]*

The Department of Mathematics at the University of California, Los Angeles, is inviting applications for the position of an Academic Administrator who will serve as the Director of the UCLA Endowed Olga Radko Math Circle (ORMC). The Academic Administrator will have the broad responsibility for administration of the ORMC, an outreach program with weekly activities for mathematically inclined students in grades K-12. Currently, over 300 children take part in the program each weekend. Instruction is delivered by a team of over 50 docents, the majority of whom are UCLA undergraduate and graduate students.

The Academic Administrator is required to teach three mathematics courses in the undergraduate curriculum per academic year as assigned by the Department. This is also intended to help with the recruitment of UCLA students as docents and instructors for the ORMC.

As the director of ORMC, the Academic Administrator will have primary responsibility for all aspects of ORMC operations:

- Determining the structure of ORMC, including the number and levels of groups
- Recruiting, training and supervising instructors, docents, and postdoctoral fellows associated with the ORMC
- Developing curricular materials and providing leadership in development of innovative ways of explaining mathematical ideas to school children
- Working with the Mathematics Department finance office to ensure timely payment of stipends and wages to ORMC instructors and docents, as appropriate
- Maintaining ORMC budget and budgetary projections, ensuring that the funds are used appropriately and efficiently for ORMC activities, and applying for grants as appropriate to fund the operations of ORMC
- Working with the Steering Committee and UCLA Development to raise funds for ORMC, both from families whose children participate in ORMC and other sources
- Admitting students to ORMC, ensuring appropriate placement, and working to maintain a collegial and inclusive atmosphere conducive to learning for all ORMC attendees
- Reporting to and working with the ORMC Steering Committee throughout the year

A competitive candidate should have leadership potential and experience with developing mathematical teaching materials for the use of gifted school children, as well as experience with teaching undergraduate mathematics courses. Candidates must have a Ph.D. degree (or equivalent) or expect to complete their Ph.D. by June 30, 2021.

Applications should be received by March 15, 2021. Further details on the position and the application process can be found at the application page.

Just a short announcement that next quarter I will be continuing the recently concluded 246A complex analysis class as 246B. Topics I plan to cover:

- Schwartz-Christoffel transformations and the uniformisation theorem (using the remainder of the 246A notes);
- Jensen’s formula and factorisation theorems (particularly Weierstrass and Hadamard); the Gamma function;
- Connections with the Fourier transform on the real line;
- Elliptic functions and their relatives;
- (if time permits) the Riemann zeta function and the prime number theorem.

Notes for the later material will appear on this blog in due course.

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 tklowden@gmail.com.

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:

- Online seminars (curated by Ao Sun and Mingchen Xia at MIT)
- Algebraic Combinatorics Online Seminars (maybe using the same data set as the preceding link?)
- Online mathematics seminars (curated by Dan Isaksen at Wayne State University)
- Math seminars (run by Edgar Costa and David Roe at MIT)

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:

- 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 [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.)

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