ISSN 0002-9920 (print) ISSN 1088-9477 (online) Notices ofof the American MathematicalMathematical Society August 2019 Volume 66, Number 7 The cover design is based on imagery from Algebraic and Topological Tools in Linear Optimization, page 1023. Cal fo Nomination AWM–AMS NOETHER LECTURE The Association for Women in Mathematics (AWM) established the Emmy Noether Lectures in 1980 to honor women who have made fundamental and sustained contributions to the mathematical sciences. In April 2013 this one-hour expository lecture was renamed the AWM–AMS Noether Lecture. The first jointly sponsored lecture was held in January 2015 at the Joint Mathematics Meetings (JMM) in San Antonio, Texas. Emmy Noether was one of the great mathematicians of her time, someone who worked and struggled for what she loved and believed in. Her life and work remain a tremendous inspiration. Additional past Noether lecturers can be found at https://awm-math.org/awards/noether-lectures. A nomination should include: a letter of nomination, a curriculum vitae of the candidate—not to exceed three pages, and a one-page outline of the nominee’s contribution to mathematics, giving four of her most important papers and other relevant information. Nominations are accepted annually from September 1 through October 15. Nominations will remain active for an additional two years after submission. The nomination procedure is described here: https://awm-math.org/awards /noether-lectures. If you have questions, call 401-455-4042 or email [email protected]. From the AMS Secretary ATTENTION ALL AMS MEMBERS Voting Information for 2019 AMS Election V URR OOT AMS members who have chosen to vote online will receive an U TE O E email message on or shortly after August 19, 2019, from the AMS YO Election Coordinator, Survey & Ballot Systems. Y The From line will be “AMS Election Coordinator”, the Sender email address will be [email protected], and the Subject CC ! line will be “AMS 2019 Election—login information below”. If O S! you use a spam lter you may want to use the above address or U TTS subject information to con gure your spam lter to ensure this UNN email will be delivered to you. The body of the message will provide your unique voting login information and the address (URL) of the voting website. AMS members who have chosen to vote by paper should expect to receive their ballot by the middle of September. Unique vot- ing login information will be printed on the ballot should you wish to vote online. At midnight (US Eastern Time) on November 1, 2019, the web- site will stop accepting votes. Paper ballots received after this date will not be counted. Additional information regarding the 2019 AMS Election is available on the AMS website: www.ams.org/election-info or by contacting the AMS: [email protected], 800.321.4267, extension 4128 (US & Canada), 401.455.4128 (worldwide). Thank you and . please remember to vote. Carla D. Savage To learn more visit: www.ams.org/election-info A WORD FROM... David Jerison, AMS Vice President I am writing to discuss with you how our community should adapt as it grows and spreads beyond my own ability to grasp. I believe that we live in a golden age of mathematics. There are more mathematicians than ever, and rather than running out of research problems to solve or getting permanently stuck in most of them, we keep finding new connections; the outside world keeps demanding more of us. At the same time, it has become harder for young mathematicians to progress in their careers. Given the projected number of tenure track positions relative to the number of PhDs, we can expect this trend to persist. Other issues, such as how we deliver education, professional training, access, and fairness, and how we learn about mathematics outside of our own specialties, always need the attention of the AMS. I will be concentrating on the career issue. Photo is courtesy of David Jerison. of David Photo is courtesy One virtue of the environment for mathematicians in the US is how disorganized it is. In other countries, whole cohorts of mathematicians can have their schooling and careers determined by a government initiative or the absence thereof. The US job market is too incoherent for that. There is, however, such a thing as too much chaos. The AMS has tempered some of the piecemeal aspects of the academic job market with MathJobs.Org. I wish there were such a system for graduate school applications. Perhaps we can cooperate to create one out of the existing AMS MathPrograms.Org site, where universities have begun listing programs at all levels. [See sidebar on facing page.] While academic career services remain central to the AMS, the Society needs to develop new mechanisms and resources for the expanding mathematical job market outside academia. It can use assistance and suggestions from job seekers and employers. The April Notices featured several essays about jobs outside of academia in the new Early Career section that I recommend to everyone. We could use dozens more like them. I also call your attention to the blogs at the AMS site https://blogs.ams.org, which include discussions of academic careers. We should be comparing notes on how each institution is dealing with the current job territory. In my de- partment at MIT, some current graduate students have taken the initiative to advise their peers on how to get job interviews. We have invited alumni(ae) back to explain their experiences. What is happening in your department? I am optimistic that as more mathematicians of all types work in industrial settings, those career paths will become easier to pursue. I also think that we as teachers will find it easier to explain the relevance of many math- ematical ideas. Moreover, I expect that with this sociological change, even so-called pure mathematicians will be swept up in new streams of research and new perspectives on old questions. In The Music Man, the stage is set with the lament that it’s “different than it was” and the rejoinder “No it ain’t, no it ain’t, but you gotta know the territory.” In my view it is, indeed, different now, and we have to learn to nav- igate the new territory collectively. David Jerison is a professor of mathematics at the Massachusetts Institute of Technology and a vice president of the American Mathematical Society. His email address is [email protected]. 994 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 66, NUMBER 7 MathPrograms.Org • MathPrograms.Org is a website for collecting applications to mathematical programs serving populations that range from high school students through graduate students to senior researchers. Sponsored by the AMS in cooperation with the Duke University Department of Mathematics, it is a clone of MathJobs.Org, and many of its features will be familiar to users of that system. • MathPrograms.Org allows programs to collect all application materials at a single site. Applicants can upload any documents specified by the program and answer any set of questions the program chooses to ask. Letter-writers can upload confidential letters of recommendation, which applicants can mark for inclusion in their applications to a particular program. Each program designates the individuals who can access the applications for the purpose of reading and rating them, and confidential EEO information can be collected and made available to designated individuals. Responses to applicants can also be made through the system. • MathPrograms.Org is convenient for applicants, who register once and then can apply to any program on the site, and for letter-writers, who need upload each letter only once, no matter how many applications it is used for. Read- ers can access all application materials at a single site, and application documents and data can be downloaded. • There are currently 63 groups or programs using MathPrograms.Org, including REUs, grant programs, institutes, and honors of various kinds. Some institutions use the system for graduate admissions, since its features are well suited to that task. In 2019-2020 the fee will be $310 for one program and $590 for up to seven programs. With the univer- sity’s cooperation, it is possible to upload information from MathPrograms.Org to university application systems. For more information about MathPrograms.Org, contact Kim Kuda in the AMS Professional Programs Department at [email protected] or 800-321-4267, ext. 4096. AUGUST 2019 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 995 August 2019 Notices Cover Credit: The image used in the cover design of the American Mathematical Society was created by Jesús A. De Loera. FEATURED ALSO IN THIS ISSUE 994 A Word from... David Jerison Features 1001 Computability and Randomness Rod Downey and Denis R. Hirschfeldt 1013 Waves, Spheres, and Tubes A Selection of Fourier Restriction Problems, Methods, and Applications Betsy Stovall 842 An Invitation to Nonstandard Analysis 1023 and its Recent Applications Algebraic and Topological Tools Isaac Goldbring and Sean Walsh in Linear Optimization Early Career: Teaching Jesús A. De Loera 1045 Why Do We Teach? Colin Adams 1047 Thoughts on Helping Students to Feel Included Jessica Sidman 1048 Teaching at a Community College Jasmine Ng 1050 Inquiry Based Learning Hanna Bennett 1052 Lessons Learned Mentoring Senior Theses 1034 Jennifer R. Bowen Attitudes of K-theory 1054 On-the-Job Teacher Training Doris Gluck and Herman Gluck Topological, Algebraic, Combinatorial Inna Zakharevich Memorial Tribute 1058 Peter Swinnerton-Dyer (1927–2018) Bryan Birch, John Coates, Jean-Louis Colliot-Thélène, and Alexei Skorobogatov Opinion 1079 Mental Health in the Mathematics Community Mikael Vejdemo-Johansson, Justin Curry, and Julie Corrigan 1085 MathJobs at the University of California–R.I.P.