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:



Dimitris Koukoulopoulos, Erdős's integer dilation approximation problem
(University of Montreal)

Thursday, April 17, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, April 18, 2025 (1am AEST, 3am NZST)

Abstract: Let $\mathcal{A}\subset\mathbb{R}_{\geqslant1}$ be a countable set such that $\limsup_{x\to\infty}\frac{1}{\log x}\sum_{\alpha\in\mathcal{A}\cap[1,x]}\frac{1}{\alpha}>0$. Erdős conjectured in 1948 that, for every $\varepsilon>0$, there exist infinitely many pairs $(\alpha, \beta)\in \mathcal{A}^2$ such that $\alpha\neq \beta$ and $|n\alpha-\beta| <\varepsilon$ for some positive integer $n$. When $\mathcal{A}$ is a set of integers, the conjecture follows by work of Erdős and Behrend on primitive sets of integers from the 1930s. Moreover, if $\mathcal{A}$ contains ``enough elements" all of pairwise ratios are irrational, then Haight proved Erdős's conjecture in 1988. In this talk, I will present recent joint work with Youness Lamzouri and Jared Duker Lichtman that solves the conjecture in full generality. A critical role in the proof is played by the machinery of GCD graphs, which were introduced by Koukoulopoulos-Maynard in the proof of the Duffin--Schaeffer conjecture in Diophantine approximation.

Upcoming talks:

Matthew de Courcy-Ireland, Cubic surfaces of Markoff type
(Stockholm University)

Thursday, April 24, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, April 25, 2025 (1am AEST, 3am NZST)

Abstract: The Markoff surface is a cubic surface with the special feature that it is only quadratic in each variable separately. Exchanging the two roots of such a quadratic produces new solutions from old, which enabled A. A. Markoff (senior) to find all the integer solutions. More recently, since work of J. Bourgain, A. Gamburd, and P. Sarnak, it has become possible to understand how the integer solutions are related to the solutions modulo primes. Given a large prime modulus, all solutions to the congruence can be shown to lift to integer solutions by combining their work with a complementary result of W. Y. Chen, which has recently been given a new proof by D. E. Martin. The talk will survey some of these developments, including some work in progress joint with Matthew Litman and Yuma Mizuno where we adapt Martin's proof to a wider family of surfaces.


Vivian Kuperberg, TBA
(ETH Zürich)

Thursday, May 1, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, May 2, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Martin Widmer, TBA
(Royal Holloway, University of London)

Thursday, May 8, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, May 9, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Peter Koymans, TBA
(Utrecht University)

Thursday, May 15, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, May 16, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Carlo Pagano, TBA
(Concordia University)

Thursday, May 22, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, May 23, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Fabien Pazuki, TBA
(University of Copenhagen)

Thursday, May 29, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, May 30, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Will Sawin, TBA
(Princeton University)

Thursday, June 5, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, June 6, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Oliver Roche-Newton, TBA
(Johannes Kepler University)

Thursday, June 12, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, June 13, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Davide Lombardo, TBA
(University of Pisa)

Thursday, June 19, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, June 20, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Jan Hendrik Bruinier, TBA
(TU Darmstadt)

Thursday, June 26, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, June 27, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Summer Break
(1 July - 31 August)


Rafael von Känel, TBA
(Institute for Advanced Study, Tsinghua University)

Thursday, September 18, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, September 19, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Sponsors:

We gratefully acknowledge the generous support of: