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
YouTube Channel: https://www.youtube.com/@numbertheorywebseminar
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:
Asif Zaman, The least prime in the Chebotarev density theorem for symmetric groups and more
(University of Toronto)
(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)
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)
(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)
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)
(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)
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)
(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)
Friday, January 24, 2025 (12am CST, 3am AEDT, 5am NZDT)
Abstract: TBA
Hector Pasten, TBA
(Pontificia Universidad Católica de Chile)
(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)
Friday, January 31, 2025 (12am CST, 3am AEDT, 5am NZDT)
Abstract: TBA
Alex Kontorovich, TBA
(Rutgers University)
(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)
Friday, February 7, 2025 (12am CST, 3am AEDT, 5am NZDT)
Abstract: TBA
Valérie Berthé, TBA
(IRIF, Université Paris Cité)
(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)
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)
(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)
Friday, February 28, 2025 (12am CST, 3am AEDT, 5am NZDT)
Abstract: TBA
Péter Varjú, TBA
(University of Cambridge)
(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)
Friday, March 7, 2025 (12am CST, 3am AEDT, 5am NZDT)
Abstract: TBA
Florian Karl Richter, TBA
(EPFL)
(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)
Friday, March 14, 2025 (12am CST, 3am AEDT, 5am NZDT)
Abstract: TBA
Gergely Harcos, TBA
(Alfréd Rényi Institute of Mathematics)
(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)
Friday, March 21, 2025 (12am CST, 3am AEDT, 5am NZDT)
Abstract: TBA
Andreas Strömbergsson, TBA
(Uppsala University)
(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)
(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)
Friday, April 4, 2025 (2am AEDT, 4am NZDT)
Abstract: TBA
Mayank Pandey, TBA
(Princeton University)
(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)
Friday, April 11, 2025 (1am AEST, 3am NZST)
Abstract: TBA
Dimitris Koukoulopoulos, TBA
(University of Montreal)
(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)
Friday, April 18, 2025 (1am AEST, 3am NZST)
Abstract: TBA
Matthew de Courcy-Ireland, TBA
(Stockholm University)
(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)
Friday, April 25, 2025 (1am AEST, 3am NZST)
Abstract: TBA
Vivian Kuperberg, TBA
(ETH Zürich)
(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)
Friday, May 2, 2025 (1am AEST, 3am NZST)
Abstract: TBA
Martin Widmer, TBA
(Royal Holloway, University of London)
(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)
Friday, May 9, 2025 (1am AEST, 3am NZST)
Abstract: TBA
Sponsors:
We gratefully acknowledge the generous support of:
University of Basel (financial support, zoom licence)
University of New South Wales (financial support, zoom licence)
Max Planck Institute for Mathematics (zoom licence, 2020)