LATEST NEWS: The Stark-SIC seminar resumes on 13th October 2026. See details below.
Welcome Back!
The Seminar restarts on 13th October 2026, continuing on alternate Tuesdays. Details of the first few talks are below.
Please note the new usual start time this year which is half-an-hour earlier than last year:
11:00 Eastern (US) / 16:00 UK / 17:00 Central Europe
Talks will typically last for 50 minutes plus 10 minutes of questions from the audience.
Upcoming Talks
Date: 13th October, 2026
Time: 11:00 Eastern (US) Time (Daylight Savings) / 16:00 British Summer Time / 17:00 Central European Time (Daylight Savings)
Title: Real quadratic fields and quantum dilogs
Speaker: Campbell Wheeler
Abstract: I will explain why values of Faddeev’s quantum dilogarithm at real quadratic units satisfy an explicit and overdetermined set of equations agreeing—after a small tweak—with Andersen-Kashaev’s notion of a quantum dilogarithm on a product of two cyclic groups. Clearly, but miraculously, this variety has points, and I will explain why it is in fact 0-dimensional. This proves the algebraicity of Stark’s conjecture for real quadratic fields. This is based on joint work with Danylo Radchenko.
Date: 27th October, 2026
Time: 12:00 Eastern (US) Time (Daylight Savings) / 16:00 Greenwich Mean time / 17:00 Central European Time
Please note the unusual time in most of the US and Canada for this talk. (The clocks will not have gone back there yet; they will have in the UK and Europe.)
Title and Speaker: TBA
Date: 10th November 2026
Time: 11:00 Eastern (US) Time / 16:00 Greenwich Mean time / 17:00 Central European Time
Title: Conference Signals
Speakers: Joseph Iverson (Iowa State) and Kean Fallon (Iowa State)
Subject Matter of the Seminar
The first part of the seminar title refers to the S-units of global fields predicted by the well-known rank-1, complex Stark conjecture for abelian L-functions (cf Tate's book Les Conjectures de Stark sur les Fonctions L d'Artin en s=0, Birkhauser, 1984). They have strong connections to Hilbert's 12th problem/explicit abelian class field theory.
The second part of the title refers to SIC-POVMs (in brief, maximal equiangular sets of lines in C^d). Research into SICs originated in quantum information theory and finite frame theory, and that work is less well-known to number theorists. It has, however, burgeoned over the last 25 years, driven in part by Zauner's 1999 conjecture and extensive computational work by Grassl, Scott et al. which revealed apparent links to Stark units on the one hand and to the representations of finite Heisenberg groups and their automorphism groups on the other.
The third part of the title refers to the fact that the seminar is also open to talks on a variety of topics related to the above two main themes. A non-exhaustive list might include: other (e.g., p-adic) aspects of Stark's conjectures and/or Hilbert's 12th Problem, Theta functions, L-function values, Related cocycles on SL_2(Z) and similar groups, Weil representations, Quantum designs, Mutually unbiased bases (MUBs).....
Slides of last year's talks displaying the range of topics in 2025/6 can be found here
Please note: his is a research seminar. Talks containing both published work and work in progress are welcome. An atmosphere of discussion is encouraged.
Past talks this year (2026/7): slides, recordings etc (where available)