Number Theory Web Seminar

This number theory seminar is purely online. Our talks come from various corners of the field and of the world. They are streamed live on Zoom.

Organizers:

  • Michael Bennett (University of British Columbia)

  • Philipp Habegger (University of Basel)

  • Alina Ostafe (UNSW Sydney)


There are no fees, but registration is necessary. To register please follow this link.

Registered users will receive an email a few hours before the talk with a link to the Zoom meeting.

The seminar runs every Thursday. Please note the usual times of the seminar below and in the FAQ Section.

Talks are usually 50 minutes and then time for some questions.

Contact: ntweb.seminar@gmail.com

Please consider the following:

  • Each talk has a unique Zoom meeting-ID that all registered participants receive by email before the talk. You will receive this email from organizers@ntwebseminar.org. Never publicly share this ID or the password.

  • If you did not received an invitation one hour before the talk please check your spam folder. If you cannot find the email there please contact ntweb.seminar@gmail.com.

  • Some mail servers are blocking our domain. Registered participants can click here to get the link to the next talk.

  • To unsubscribe from the mailing list please follow the link at the bottom of the invitation email.

  • Participant's audio is muted by default. You can unmute to ask questions.

  • You can ask questions in the chat window or by unmuting the microphone and asking them directly.

Next talk:



Larry Guth, Reflections on the proof(s) of the Vinogradov mean value conjecture
(MIT)


Thursday, January 27, 2022 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, January 28, 2022 (12am CST, 3am AEDT, 5am NZDT)

Abstract: The Vinogradov mean value conjecture concerns the number of solutions of a system of diophantine equations. This number of solutions can also be written as a certain moment of a trigonometric polynomial. The conjecture was proven in the 2010s by Bourgain-Demeter-Guth and by Wooley, and recently there was a shorter proof by Guo-Li-Yang-Zorin-Kranich. The details of each proof involve some intricate estimates. The goal of the talk is to try to reflect on the proof(s) in a big picture way. A key ingredient in all the proofs is to combine estimates at many different scales, usually by doing induction on scales. Why does this multi-scale induction help? What can multi-scale induction tell us and what are its limitations?


Upcoming talks:

Peter Humphries, L^p-norm bounds for automorphic forms
(University of Virginia)


Thursday, February 3, 2022 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, February 4, 2022 (12am CST, 3am AEDT, 5am NZDT)

Abstract: A major area of study in analysis involves the distribution of mass of Laplacian eigenfunctions on a Riemannian manifold. A key result towards this is explicit L^p-norm bounds for Laplacian eigenfunctions in terms of their Laplacian eigenvalue, due to Sogge in 1988. Sogge's bounds are sharp on the sphere, but need not be sharp on other manifolds. I will discuss some aspects of this problem for the modular surface; in this setting, the Laplacian eigenfunctions are automorphic forms, and certain L^p-norms can be shown to be closely related to certain mixed moments of L-functions. This is joint with with Rizwanur Khan.


Zeev Rudnick, Beyond uniform distribution
(Tel Aviv University)


Thursday, February 10, 2022 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, February 11, 2022 (12am CST, 3am AEDT, 5am NZDT)

Abstract: The study of uniform distribution of sequences is more than a century old, with pioneering work by Hardy and Littlewood, Weyl, van der Corput and others. More recently, the focus of research has shifted to much finer quantities, such as the distribution of nearest neighbor gaps and the pair correlation function. Examples of interesting sequences for which these quantities have been studied include the zeros of the Riemann zeta function, energy levels of quantum systems, and more. In this expository talk, I will discuss what is known about these examples and discuss the many outstanding problems that this theory has to offer.


Harry Schmidt, tba
(University of Basel)


Thursday, February 17, 2022 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, February 18, 2022 (12am CST, 3am AEDT, 5am NZDT)

Abstract: tba


Nicole Looper, tba
(Brown University)


Thursday, February 24, 2022 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, February 25, 2022 (12am CST, 3am AEDT, 5am NZDT)

Abstract: tba


Ekin Özman, tba
(Boğaziçi University)


Thursday, March 3, 2022 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, March 4, 2022 (12am CST, 3am AEDT, 5am NZDT)

Abstract: tba


Dmitry Kleinbock, tba
(Brandeis University)


Thursday, March 10, 2022 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, March 11, 2022 (12am CST, 3am AEDT, 5am NZDT)

Abstract: tba


Aaron Levin, tba
(Michigan State University)


Thursday, March 17, 2022 (9am PDT, 12pm EDT, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, March 18, 2022 (12am CST, 3am AEDT, 5am NZDT)

Abstract: tba


Winnie Li, tba
(Pennsylvania State University)


Thursday, March 24, 2022 (9am PDT, 12pm EDT, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, March 25, 2022 (12am CST, 3am AEDT, 5am NZDT)

Abstract: tba


William Chen, tba
(Institute for Advanced Study)


Thursday, March 31, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, April 1, 2022 (2am AEDT, 4am NZDT)

Abstract: tba


Ana Caraiani, tba
(Imperial College London)


Thursday, April 7, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, April 8, 2022 (1am AEST, 3am NZST)

Abstract: tba


Ram Murty, tba
(Queen's University)


Thursday, April 14, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, April 15, 2022 (1am AEST, 3am NZST)

Abstract: tba



Joni Teräväinen, tba
(University of Turku)


Thursday, April 21, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, April 22, 2022 (1am AEST, 3am NZST)

Abstract: tba


Barry Mazur, tba
(Harvard University)


Thursday, April 28, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, April 29, 2022 (1am AEST, 3am NZST)

Abstract: tba


Levent Alpöge, tba
(Harvard University)


Thursday, May 5, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, May 6, 2022 (1am AEST, 3am NZST)

Abstract: tba


Andrew Granville, tba
(Université de Montréal)


Thursday, May 12, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, May 13, 2022 (1am AEST, 3am NZST)

Abstract: tba


Yunqing Tang, tba
(Princeton University)


Thursday, May 26, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, May 27, 2022 (1am AEST, 3am NZST)

Abstract: tba


Elon Lindenstrauss, tba
(Hebrew University of Jerusalem)


Thursday, June 2, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, June 3, 2022 (1am AEST, 3am NZST)

Abstract: tba


Sponsors:

We gratefully acknowledge the generous support of:

  • University of Basel (financial support, zoom licence)

  • Max Planck Institute for Mathematics (zoom licence, 2020)

  • University of New South Wales (zoom licence)