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:


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

YouTube Channel: https://www.youtube.com/@numbertheorywebseminar 

Please consider the following:

Next talk:



Misha Rudnev, The sum-product problem for integers with few prime factors
(University of Bristol)

Thursday, December 7, 2023 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, December 8, 2023 (12am CST, 3am AEDT, 5am NZDT)

Abstract: It was asked by Szemerédi if the known sum-product estimates can be improved for a set of N integers under the constraint that each integer has a small number of prime factors. We prove, if the maximum number of prime factors for each integer is sub-logarithmic in N, the sum-product exponent 5/3-o(1). 

This becomes a corollary of an additive energy versus the product set cardinality estimate, which turns out to be the best possible. 

It is based on a scheme of Burkholder-Gundy-Davis martingale square function inequalities in p-adic scales, followed by an application of a variant of the Schmidt subspace theorem.

Upcoming talks:

Djordje Milićević, Beyond the spherical sup-norm problem
(Bryn Mawr College)

Thursday, December 14, 2023 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, December 15, 2023 (12am CST, 3am AEDT, 5am NZDT)

Abstract: The sup-norm problem on arithmetic Riemannian manifolds occupies a prominent place at the intersection of harmonic analysis, number theory, and quantum mechanics. It asks about the sup-norm of L^2-normalized joint eigenfunctions of invariant differential operators and Hecke operators — that is, automorphic forms — most classically in terms of their Laplace eigenvalues (as in the QUE problem for high-energy eigenstates), but also in terms of the volume of the manifold and other parameters.

In this talk, we will motivate the sup-norm problem and then describe our results, joint with Blomer, Harcos, and Maga, which for the first time solve it for non-spherical Maass forms of an increasing dimension of the associated K-type, on an arithmetic quotient of G=SL(2,C), with K=SU(2). We combine representation theory, spectral analysis, and Diophantine arguments, developing new Paley-Wiener theory for G and sharp estimates on spherical trace functions of arbitrary K-type on the way to a novel counting problem of Hecke correspondences close to various special submanifolds of G.


Zeev Rudnick, A talk in honor of Peter Sarnak's 70th birthday
(Tel Aviv University)

Celebrating Peter Sarnak's 70th birthday

Special Chair: Alex Kontorovich (Rutgers University)


Thursday, December 21, 2023 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, December 22, 2023 (12am CST, 3am AEDT, 5am NZDT)

Abstract: I will give selected highlights of Peter Sarnak's works on automorphic forms and some of the outstanding problems remaining.


Oded Regev, TBA
(Courant Institute of Mathematical Sciences)

Thursday, January 18, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, January 19, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Thomas Tucker, TBA
(University of Rochester)

Thursday, January 25, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, January 26, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Akshat Mudgal, TBA
(University of Oxford)

Thursday, February 1, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, February 2, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Victor Y. Wang, TBA
(IST Austria)

Thursday, February 8, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, February 9, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Damaris Schindler, TBA
(Goettingen University)

Thursday, February 15, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, February 16, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Paul Pollack, TBA
(University of Georgia)

Thursday, February 22, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, February 23, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Arul Shankar, TBA
(University of Toronto)

Thursday, February 29, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, March 1, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Vesselin Dimitrov, TBA
(Georgia Institute of Technology/Caltech)

Thursday, March 7, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, March 8, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Marc Munsch, TBA
(Jean Monnet University)

Thursday, March 14, 2024 (9am PDT, 12pm EDT, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, March 15, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Javier Fresán, TBA
(Sorbonne University)

Thursday, March 21, 2024 (9am PDT, 12pm EDT, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, March 22, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Jacob Tsimerman, TBA
(University of Toronto)

Thursday, May 9, 2024 (8am PDT, 11am EDT, 4pm GMT, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, May 10, 2024 (1am AEST, 3am NZST)

Abstract: TBA


Sponsors:

We gratefully acknowledge the generous support of: