Saturday, April 27, 2019
Malott Hall, TBD
April 27–28, 2019
A primary goal of the Upstate Number Theory Conference is to bring together the specialists from the various branches of Number Theory in the Upstate New York region and surrounding areas, and to expose the younger researchers to new and old problems in the field.
For those who plan to Arrive on Friday, April 26th, Kiran Kedlaya (UCSD & IAS) will be giving a colloquium talk at 4:30pm in Malott 251. Parking information is below.
For the main Upstate Conference website go to Upstate NY Number Theory Conference.
Registration is now open! Please go to the following link Upstate NY Number Theory Registration.
Banquet registration is also required! A banquet will be held the evening of April 27th in 401/403 Physical Sciences Building. If you are interested in attending the banqute please go to https://forms.gle/KwH94zyoToZMkvDo6 to register. Please note that the banquet is capped at 60.
Abby Bourdon, Wake Forest University
Title: Isolated Points on Modular Curves
Abstract: We say a closed point on a curve C is isolated if it does not belong to an infinite family of effective divisors of degree d parametrized by the projective line or a positive rank abelian subvariety of the Jacobian of C. In this talk, we will study the image of isolated points under morphisms, giving conditions under which the image of an isolated point remains isolated. We will explore applications of this result to the case where C is the modular curve X_1(N). This work is Ozlem Ejder, Yuan Liu, Frances Odumodu, and Bianca Viray extends recent results of the same authors concerning sporadic points on modular curves.
Ling Long, Louisiana State
Title: Hypergeometric Supercongruences
Abstract: In this talk, we will discuss supercongruences occured to truncated hypergeometric series originated in the work and conjectures of Beukers and Coster. These congruences can be viewed as p-adic analogues of hypergeometric umbrella and discuss approaches to supercongruences including a p-adic perturbation method proposed in a joing work with Ravi Ramakrisha. The talk will be concluded by applications and new open conjectures baed on the motivic setting.
Aaron Pollack, Duke University
Title: Modular forms on G_2
Abstract: Classical modular forms are very special automorphic functions for the group GL(2), and similarly holomorphic Siegel modular forms are very special automorphic functions for the group GSp(2n). It turns out that the split exceptional group G_2, and certain forms of the other exceptional groups, possess a similar very special class of automorphic functions. These are called the 'modular forms', and their study was initiated by Gross-Wallach and Gan-Gross-Savin. I will define these modular forms on G_2 and explain what is known about them.
Arul Shankar, University of Toronto
Title: Families of elliptic curves ordered by conductor
Abstract: Conjectures on the statistics of elliptic curves are usually formulated with the assumption that the curves in question are ordered by their conductors. However, when proving results on the statistics of elliptic curves, the curves are usually ordered by (naive) height. There are two two reasons for doing so: first, it is difficult to rule out the possibility that there are many elliptic curves with small discriminant but large height. Second, it is difficult to rule out the possibility that there are many elliptic curves with large discriminant but small conductor. In this talk, we will focus on the second question, and prove some partial results bounding the number of elliptic curves whose discriminants are much larger than their heights. As consequences, we will construct positive proportion families of elliptic curves, and determine their asymptotics when they are ordered by conductor. We will also prove that the average size of their 2-Selmer groups is 3. This is joint work with Ananth Shankar and Xiaoheng Wang.
Brian Smithling, Johns Hopkins University
Title: On Shimura varieties for unitary groups
Abstract: Shimura varieties attached to unitary similitude groups are a well-studied class of PEL Shimura varieties (i.e., varieties admitting a moduli description in terms of abelian varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.
Preston Wake, IAS & Michigan State
Title: Eisenstein congruences and a Bloch-Kato conjecture in tame families
Abstract: A fact made famous by Mazur is that the Galois representation associated to the modular curve X_0(11) (which is an elliptic curve) is reducible modulo 5. Less famously, the representation is also reducible modulo 25. I'll talk about this extra reducibility and what it has to do with the Bloch-Kato conjecture. This is joint work with Akshay Venkatesh.
Housing information is provided by participating role, and for those requiring sign up you can do so during your registration.
Rooms have been blocked at The Hotel Ithaca for Graduate Students including those contributing talks, Invited Speakers and Organizers. A reservation sign up sheet is provided to you during your registration.
Rooms have been blocked at Best Western University Inn for regular participants. Please contact the Best Western directly to make a reservation by April 5th to receive the Cornell rate. Please indicate the conference group name "Upstate NY Number Theory Seminar" when you make your reservation.
Both hotels provide a courtesy shuttle to and from campus 7 days/week.
EVENT SCHEDULE will be posted soon. All talks and activities will be held in Malott 251, 253, 203, 207, and 224
BANQUET: A banquet will be held the evening of April 27th in 401/403 Physical Sciences Building. A separate registration will be available in April to sign up for the banquet. All registrants will be notified at that time.
PARKING: For parking on Friday afternoon, there is a parking garage (Hoy Road Parking Garage) one block south of Malott Hall with entrances on Campus Road and Hoy Road. On the Google map, the parking garage is located between two green patches (Hoy Field and Schoellkopf Field) and will appear if you zoom in a little. Also about a half mile east of Malott Hall, at the intersection of Tower road and Judd Falls road, there is a metered lot.
Visitors may park in most spots on campus on the weekend with no permit, in particular in the area around Malott Hall. Be careful of the areas marked with a moon: these are restricted at all times. Also on weekends attendees can park at both Hoy Road Parking Garage and Forest Home Garage, which is less than a block north of Malott Hall (off Forest Home Drive).
For mobility or other accommodations and for general inquiries please contact email@example.com.