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.

News: The Tuesday slots observe a break in the month of August. In September we will continue to have two talks per week.

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:



Bjorn Poonen, "Tetrahedra with rational dihedral angles"
(MIT)

Thursday, August 6, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, August 7, 2020 (1am AEST, 3am NZST)

Abstract: In 1895, Hill discovered a 1-parameter family of tetrahedra whose dihedral angles are all rational multiples of pi. In 1976, Conway and Jones related the problem of finding all such tetrahedra to solving a polynomial equation in roots of unity. Many previous authors have solved polynomial equations in roots of unity, but never with more than 12 monomials, and the Conway-Jones polynomial has 105 monomials! I will explain the method we use to solve it and our discovery that the full classification consists of two 1-parameter families and an explicit finite list of sporadic tetrahedra.

Building on this work, we classify all configurations of vectors in R^3 such that the angle between each pair is a rational multiple of pi. Sample result: Ignoring trivial families and scalar multiples, any configuration with more than 9 vectors is contained in a particular 15-vector configuration.

This is joint work with Kiran Kedlaya, Alexander Kolpakov, and Michael Rubinstein.


Upcoming talks:

Carl Pomerance, "Practical numbers"
(Dartmouth College)

Thursday, August 13, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, August 14, 2020 (1am AEST, 3am NZST)

Abstract: A practical number n is one where each number up to n can be expressed as a subset sum of n's positive divisors. It seems that Fibonacci was interested in them since they have the property that all fractions m/n with m < n can be written as a sum of distinct unit fractions with denominators dividing n. With similar considerations in mind, Srinivasan in 1948 coined the term "practical". There has been quite a lot of effort to study their distribution, effort which has gone hand in hand with the development of the anatomy of integers. After work of Tenenbaum, Saias, and Weingartner, we now know the "Practical Number Theorem": the number of practical numbers up to x is asymptotically cx/log x, where c= 1.33607.... In this talk I'll discuss some recent developments, including work of Thompson who considered the allied concept of phi-practical numbers n (the polynomial t^n-1 has divisors over the integers of every degree up to n) and the proof (joint with Weingartner) of a conjecture of Margenstern that each large odd number can be expressed as a sum of a prime and a practical number.


Christopher Skinner, tba
(Princeton University)

Thursday, August 20, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, August 21, 2020 (1am AEST, 3am NZST)

Abstract: tba


Hector Pasten, tba
(Pontificia Universidad Católica de Chile)

Thursday, August 27, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, August 28, 2020 (1am AEST, 3am NZST)

Abstract: tba


Umberto Zannier, tba
(Scuola Normale Superiore Pisa)

Tuesday, September 1, 2020 (1am PDT, 4am EDT, 9am BST, 10am CEST, 11am IDT, 1:30pm IST, 4pm China Standard Time, 6pm AEST, 8pm NZST)

Abstract: tba


Kevin Ford, tba
(University of Illinois at Urbana-Champaign)

Thursday, September 3, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, September 4, 2020 (1am AEST, 3am NZST)

Abstract: tba


Bianca Viray, tba
(University of Washington)

Thursday, September 10, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, September 11, 2020 (1am AEST, 3am NZST)

Abstract: tba


Özlem Imamoglu, tba
(ETH Zürich)

Thursday, September 17, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, September 18, 2020 (1am AEST, 3am NZST)

Abstract: tba


Emmanuel Breuillard, tba
(University of Cambridge)

Thursday, September 24, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, September 25, 2020 (1am AEST, 3am NZST)

Abstract: tba


Wei Ho, tba
(University of Michigan)

Thursday, October 1, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, October 2, 2020 (1am AEST, 3am NZST)

Abstract: tba


Philippe Michel, tba
(EPFL)

Thursday, October 8, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, October 9, 2020 (1am AEST, 3am NZST)

Abstract: tba


Cameron L. Stewart, tba
(University of Waterloo)

Thursday, October 15, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard)
Friday, October 16, 2020 (1am AEST, 3am NZST)

Abstract: tba


Sponsors:

We gratefully acknowledge the generous support of:

  • University of Basel (financial support, zoom licence)

  • Max Planck Institute for Mathematics (zoom licence)