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:

  • Mike 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.

Please note the usual dates of the seminar in the FAQ Section. Please also note the varying times in the Tuesday slot, to accommodate more time zones.

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:



Will Sawin, The distribution of prime polynomials over finite fields
(Columbia University)

Thursday, October 29, 2020 (9am PDT, 12pm EDT, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm IST)
Friday, October 30, 2020 (12am China Standard Time, 3am AEDT, 5am NZDT)

Abstract: Many conjectures in number theory have analogues for polynomials in one variable over a finite field. In recent works with Mark Shusterman, we proved analogues of two conjectures about prime numbers - the twin primes conjecture and the conjecture that there are infinitely many primes of the form +1. I will describe these results and explain some of the key ideas in the proofs, which combine classical analytic methods, elementary algebraic manipulations, and geometric methods.


Upcoming talks:

Jens Marklof, The three gap theorem in higher dimensions
(University of Bristol)

Tuesday, November 3, 2020 (2am PST, 5am EST, 10am GMT, 11am CET, 12pm Israel Standard Time, 3:30pm IST, 6pm China Standard Time, 9pm AEDT, 11pm NZDT)

Abstract: Take a point on the unit circle and rotate it N times by a fixed angle. The N points thus generated partition the circle into N intervals. A beautiful fact, first conjectured by Hugo Steinhaus in the 1950s and proved independently by Vera Sós, János Surányi and Stanisław Świerczkowski, is that for any choice of N, no matter how large, these intervals can have at most three distinct lengths. In this lecture I will explore an interpretation of the three gap theorem in terms of the space of Euclidean lattices, which will produce various new results in higher dimensions, including gaps in the fractional parts of linear forms and nearest neighbour distances in multi-dimensional Kronecker sequences. The lecture is based on joint work with Alan Haynes (Houston) and Andreas Strömbergsson (Uppsala).

  1. J. Marklof and A. Strömbergsson, The three gap theorem and the space of lattices, American Mathematical Monthly 124 (2017) 741-745 https://people.maths.bris.ac.uk/~majm/bib/threegap.pdf

  2. A. Haynes and J. Marklof, Higher dimensional Steinhaus and Slater problems via homogeneous dynamics, Annales scientifiques de l'Ecole normale superieure 53 (2020) 537-557 https://people.maths.bris.ac.uk/~majm/bib/steinhaus.pdf

  3. A. Haynes and J. Marklof, A five distance theorem for Kronecker sequences, preprint arXiv:2009.08444 https://people.maths.bris.ac.uk/~majm/bib/steinhaus2.pdf


Pär Kurlberg, Distribution of lattice points on hyperbolic circles
(KTH)

Thursday, November 5, 2020 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm IST)
Friday, November 6, 2020 (12am China Standard Time, 3am AEDT, 5am NZDT)

Abstract: We study the distribution of lattice points lying on expanding circles in the hyperbolic plane. The angles of lattice points arising from the orbit of the modular group PSL(2,Z), and lying on hyperbolic circles centered at i, are shown to be equidistributed for generic radii (among the ones that contain points). We also show that angles fail to equidistribute on a thin set of exceptional radii, even in the presence of growing multiplicity. Surprisingly, the distribution of angles on hyperbolic circles turns out to be related to the angular distribution of euclidean lattice points lying on circles in the plane, along a thin subsequence of radii. This is joint work with D. Chatzakos, S. Lester and I. Wigman.


Gérald Tenenbaum, Recent progress on the Selberg-Delange method in analytic number theory
(Université de Lorraine)

Tuesday, November 10, 2020 (2am PST, 5am EST, 10am GMT, 11am CET, 12pm Israel Standard Time, 3:30pm IST, 6pm China Standard Time, 9pm AEDT, 11pm NZDT)

Abstract: Link


David Masser, Pencils of norm form equations and a conjecture of Thomas
(University of Basel)

Thursday, November 12, 2020 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm IST)
Friday, November 13, 2020 (12am China Standard Time, 3am AEDT, 5am NZDT)

Abstract: We consider certain one-parameter families of norm form (and other) diophantine equations, and we solve them completely and uniformly for all sufficiently large positive integer values of the parameter (everything effective), following a line started by Emery Thomas in 1990. The new tool is a bounded height result from 2017 by Francesco Amoroso, Umberto Zannier and the speaker.


Jason Bell, A transcendental dynamical degree
(University of Waterloo)

Monday, November 16, 2020 (5pm PST, 8pm EST)
Tuesday, November 17, 2020 (1am GMT, 2am CET, 3am IST, 6:30am Israel Standard Time, 9am China Standard Time, 12pm AEDT, 2pm NZDT)

Abstract: The degree of a dominant rational map $f:\mathbb{P}^n\to \mathbb{P}^n$ is the common degree of its homogeneous components. By considering iterates of $f$, one can form a sequence $\deg(f^n)$, which is submultiplicative and hence has the property that there is some $\lambda\ge 1$ such that $(\deg(f^n))^{1/n}\to \lambda$. The quantity $\lambda$ is called the first dynamical degree of $f$. We’ll give an overview of the significance of the dynamical degree in complex dynamics and describe an example in which this dynamical degree is provably transcendental. This is joint work with Jeffrey Diller and Mattias Jonsson.


Chantal David, tba
(Concordia University)

Thursday, November 19, 2020 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm IST)
Friday, November 20, 2020 (12am China Standard Time, 3am AEDT, 5am NZDT)

Abstract: tba


Jasmin Matz, tba
(University of Copenhagen)

Tuesday, November 24, 2020 (2am PST, 5am EST, 10am GMT, 11am CET, 12pm Israel Standard Time, 3:30pm IST, 6pm China Standard Time, 9pm AEDT, 11pm NZDT)

Abstract: tba


Michael Stoll, tba
(University of Bayreuth)

Thursday, November 26, 2020 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm IST)
Friday, November 27, 2020 (12am China Standard Time, 3am AEDT, 5am NZDT)

Abstract: tba


Dragos Ghioca, tba
(University of British Columbia)

Monday, November 30, 2020 (5pm PST, 8pm EST)
Tuesday, December 1, 2020 (1am GMT, 2am CET, 3am IST, 6:30am Israel Standard Time, 9am China Standard Time, 12pm AEDT, 2pm NZDT)

Abstract: tba


Rachel Pries, tba
(Colorado State University)

Thursday, December 3, 2020 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm IST)
Friday, December 4, 2020 (12am China Standard Time, 3am AEDT, 5am NZDT)

Abstract: tba


Jacob Tsimerman, tba
(University of Toronto)

Monday, December 7, 2020 (5pm PST, 8pm EST)
Tuesday, December 8, 2020 (1am GMT, 2am CET, 3am IST, 6:30am IST, 9am CST, 12pm AEDT, 2pm NZDT)

Abstract: tba


Maksym Radziwill, tba
(California Institute of Technology)

Thursday, December 10, 2020 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm IST)
Friday, December 11, 2020 (12am China Standard Time, 3am AEDT, 5am NZDT)

Abstract: tba


Adam Harper, tba
(University of Warwick)

Tuesday, December 15, 2020 (2am PST, 5am EST, 10am GMT, 11am CET, 12pm Israel Standard Time, 3:30pm IST, 6pm China Standard Time, 9pm AEDT, 11pm NZDT)

Abstract: tba


Gisbert Wüstholz, tba
(ETH / University Zurich)


Thursday, December 17, 2020 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm IST, 9:30pm IST)
Friday, December 18, 2020 (12am CST, 3am AEDT, 5am NZDT)

Abstract: tba

Jianya Liu, tba
(Shandong University)

Tuesday, December 22, 2020 (2am PST, 5am EST, 10am GMT, 11am CET, 12pm Israel Standard Time, 3:30pm IST, 6pm China Standard Time, 9pm AEDT, 11pm NZDT)

Abstract:


Alexander Lubotzky, tba
(Hebrew University of Jerusalem)


Thursday, January 7, 2021 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm IST, 9:30pm IST)
Friday, January 8, 2021 (12am CST, 3am AEDT, 5am NZDT)

Abstract: tba


Sponsors:

We gratefully acknowledge the generous support of:

  • University of Basel (financial support, zoom licence)

  • Max Planck Institute for Mathematics (zoom licence)