Oregon Number Theory Days
A triannual number theory seminar rotating between Oregon State University,
Portland State University, and the University of Oregon
Upcoming meeting:
Recent past meeting:
Registration:
Please complete the very short registration form by October 6, 2022.
Speakers:
Lea Beneish, University of California–Berkeley
Alexandra Florea, University of California–Irvine
Dinakar Ramakrishnan, California Institute of Technology
Claus Sorensen, University of California–San Diego
Schedule:
09:45-10:00 Check-in
10:00-10:50 Dinakar Ramakrishnan: L-series, non-vanishing, its significance, and examples - Part I (slides)
10:50-11:00 Break
11:00-11:50 Alexandra Florea: Negative moments of the Riemann zeta function
Abstract: I will talk about recent work towards a conjecture of Gonek regarding negative shifted moments of the Riemann zeta function. I will explain how to obtain asymptotic formulas when the shift in the Riemann zeta function is big enough, and how we can obtain non-trivial upper bounds for smaller shifts. Joint work with H. Bui.
11:50-12:00 Break
12:00-12:50 Claus Sorensen: Rigid vectors in principal series
Abstract: This talk is on joint work with Aranya Lahiri. For large primes p we promote pro-p Iwahori subgroups to rigid analytic groups. This allows us to talk about the rigid vectors in p-adic principal series representations for an arbitrary split reductive group. I will present an irreducibility criterion which generalizes a result of Clozel and Ray for general linear groups. A sizeable portion of the talk will be a gentle introduction to the subject accessible to advanced undergraduates.
1:00-2:30 Lunch Break
2:30-3:20 Claus Sorensen: Duals and admissibility mod p
Abstract: This talk is on joint work with Peter Schneider. Our context here is the category of smooth mod p representations of a p-adic Lie group G. In contrast to the complex case the smooth dual is often zero, which naturally leads to consider its derived functors. We package these in a single duality functor on the derived category D(G) and use it to compare different notions of an admissible complex of representations. At least the first half will be colloquial and is intended for a general audience.
3:20-3:30 Break
3:30-4:20 Lea Beneish: The Gross--Kohnen--Zagier formula via p-adic uniformisation
Abstract: The Gross-Kohnen-Zagier theorem says that certain generating series of CM points are modular forms of weight 3/2 in the Jacobian of the modular curve X_0(N). In this talk, I will discuss a new proof of the Gross--Kohnen--Zagier formula for Shimura curves which uses the p-adic uniformisation of Cerednik--Drinfeld. The explicit description of CM points via this uniformisation leads to an expression for the Gross--Kohnen--Zagier generating series as the ordinary projection of the first derivative of a p-adic family of positive definite ternary theta series. This is joint work with Henri Darmon, Lennart Gehrmann and Marti Roset Julia.
4:20-4:30 Break
4:30-5:20 Dinakar Ramakrishnan: L-series, non-vanishing, its significance, and examples - Part II (slides)
Funding:
There are very limited funds available to provide support for travel; when you register, let us know what funding you need. We expect to reimburse most ground transportation expenses, and priority will be given to regional students.
If your attendance is predicated on a significant amount of travel support (e.g., airfare) you are advised to contact the organizers before registering.
For a list of local lodging options, see PSU's list of local lodging options.
For questions about financial support, please feel free to email Liubomir Chiriac at chiriac(at)pdx(dot)edu.
Parking and local information:
Parking for non-PSU employees is available at Parking Structure 1 (1872 SW Broadway), approximately 269 feet from the venue.
Organizers:
Liubomir Chiriac, Portland State University
Derek Garton, Portland State University
Contact the organizers: oregonnumbertheorydays@gmail.com
Support has been provided by:
National Security Agency
The banner photo is by photographer Michael McCullough and is used under its creative commons license. The photo can be found at https://www.flickr.com/photos/ex_magician/1959699192/in/photostream/