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:



Asif Zaman, The least prime in the Chebotarev density theorem for symmetric groups and more
(University of Toronto)

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

Abstract: Let $K/k$ be a Galois extension of number fields with Galois group $G$. For a conjugacy class $C$ of $G$, the least unramified prime with Frobenius element in $C$ is known to be at most a fixed absolute power of the discriminant of $K$ due to the celebrated work of Lagarias, Montgomery, and Odlyzko (1979). This theorem has been extensively studied with the primary method exploiting statistics of zeros of L-functions. The current record for the exponent is 16 due to Kadiri, Ng, and Wong (2019). For $G = S_n$, I will describe a method based on detecting sign changes that improves this exponent to decay exponentially with $n$ as $n \to \infty$.  The ideas also apply to other groups $G$ and conjugacy invariant subsets $C$.

This talk is based on joint work with Peter Cho and Robert Lemke Oliver.


Upcoming talks:

Katharine Woo, Manin's conjecture for Châtelet surfaces
(Princeton University)

Thursday, December 12, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 8:30pm Indian Standard Time)
Friday, December 13, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: We resolve Manin's conjecture for all Châtelet surfaces over Q (surfaces given by equations of the form x^2 + ay^2 = f(z)) -- we establish asymptotics for the number of rational points of increasing height. The key analytic ingredient is estimating sums of Fourier coefficients of modular forms along polynomial values.


David Zureick-Brown, ell-adic Images of Galois for Elliptic Curves over Q
(Amherst College)

Thursday, December 19, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 8:30pm Indian Standard Time)
Friday, December 20, 2024 (12am CST, 3am AEDT, 5am NZDT)

Abstract: I will discuss recent joint work with Jeremy Rouse and Drew Sutherland on Mazur’s “Program B” — the classification of the possible “images of Galois” associated to an elliptic curve (equivalently, classification of all rational points on certain modular curves XH). The main result is a provisional classification of the possible images of l-adic Galois representations associated to elliptic curves over Q and is provably complete barring the existence of unexpected rational points on modular curves associated to the normalizers of non-split Cartan subgroups and two additional genus 9 modular curves of level 49.

I will also discuss the framework and various applications (for example: a very fast algorithm to rigorously compute the l-adic image of Galois of an elliptic curve over Q), and then highlight several new ideas from the joint work, including techniques for computing models of modular curves and novel arguments to determine their rational points, a computational approach that works directly with moduli and bypasses defining equations, and (with John Voight) a generalization of Kolyvagin’s theorem to the modular curves we study.


Katherine E. Stange, TBA
(University of Colorado, Boulder) 

Thursday, January 23, 2025 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 8:30pm Indian Standard Time)
Friday, January 24, 2025 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Hector Pasten, TBA
(Pontificia Universidad Católica de Chile)

Thursday, January 30, 2025 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 8:30pm Indian Standard Time)
Friday, January 31, 2025 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Alex Kontorovich, TBA
(Rutgers University

Thursday, February 6, 2025 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, February 7, 2025 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Valérie Berthé, TBA
(IRIF, Université Paris Cité

Thursday, February 20, 2025 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, February 21, 2025 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Shaoshi Chen, TBA
(Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Thursday, February 27, 2025 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, February 28, 2025 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Péter Varjú, TBA
(University of Cambridge

Thursday, March 6, 2025 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 8:30pm Indian Standard Time)
Friday, March 7, 2025 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Florian Karl Richter, TBA
(EPFL

Thursday, March 13, 2025 (9am PDT, 12pm EDT, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, March 14, 2025 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Gergely Harcos, TBA
(Alfréd Rényi Institute of Mathematics

Thursday, March 20, 2025 (9am PDT, 12pm EDT, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, March 21, 2025 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Andreas Strömbergsson, TBA
(Uppsala University

Thursday, March 27, 2025 (9am PDT, 12pm EDT, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)

Friday, March 28, 2025 (12am CST, 3am AEDT, 5am NZDT)

Abstract: TBA


Stephanie Chan, TBA
(IST Austria)

Thursday, April 3, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, April 4, 2025 (2am AEDT, 4am NZDT)

Abstract: TBA


Mayank Pandey, TBA
(Princeton University)

Thursday, April 10, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, April 11, 2025 (1am AEST, 3am NZST)

Abstract: TBA


Dimitris Koukoulopoulos, TBA
(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: TBA


Matthew de Courcy-Ireland, TBA
(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: TBA


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


Sponsors:

We gratefully acknowledge the generous support of: