The Schedule PLANT

Registration and Coffee outside HOA 160, 2:00-2:30

Reception outside HOA 160, 5:00-6:30

Registration 9:00-9:30

Imaginary quadratic fields with p-torsion-free class groups and specified split primes

Olivia Beckwith (Tulane University)

We study Ramanujan-type congruences for Hurwitz class numbers using harmonic Maass forms. As an application, we show that for any odd prime p and finite set  of odd primes S, there exists an imaginary quadratic field which splits at each prime in S and has class number indivisible by p. This result is in the spirit of results by Bruinier, Bhargava (when p=3) and Wiles, but the methods are completely different. This is joint work with Martin Raum and Olav Richter. 

Coffee break 10:30 - 11:00

Uncertainty Principles, restriction theory, and Applications

Alex Iosevich (University of Rochester)

We are going to discuss how the classical Heisenberg Uncertainty Principle can be improved in the presence of non-trivial restriction estimates. We are also going to describe some applications of uncertainty principles to exact signal recovery. 

Lunch 12:00 - 2:00

Coffee break 3:00 - 3:30

Lattice Covering Densities and Additive Combinatorics

Alexandria Rose (IAS)

Conference dinner at Soba, 6:30

Zeros of L-functions attached to Maass forms

Amita Malik (Penn State)

Though the study pertaining the zeros of the Riemann zeta functions goes back to the seminal paper of Riemann from 1850’s, the known results are very far from the expected truth. In theory, most of the analogous statements should be true for its cousins, generally known as L-functions, but not all is known about these functions and thus it remains an active area of research. In this talk, we focus on one such type of functions which arise from Maass forms. This talk is based on joint work with Rahul Kumar.

Coffee break 10:30 - 11:00

Lightning Talks by

• Anwar Fouad (Penn State)

• Daniel Flores (Purdue)

• Trajan Hammonds (Princeton)

• Jiaqi Hou (U Wisconsin-Madison)

• Evan O'Dorney (CMU)

• Donggeun Ryou (University of Rochester)

• Olivine Silier (UC Berkely)

• Liding Yao (Ohio State)

Moments of Dirichlet L-functions

Caroline Turnage-Butterbaugh (Carleton College)

Lunch 12:00 - 2:00

Multiple zeta values from arithmetic to geometry (slides)

Cezar Lupu (Beijing Institute of Mathematical Sciences and Applications)

In this talk, we give a survey on multiple zeta values focusing more on their applications ranging from arithmetic properties of odd zeta values to Dirichlet eigenvalues in a regular polygon. We explore various identities involving different families of multiple zeta values and we emphasize their importance in proving some very important conjectures.

Coffee break 3:00 - 3:30

Career panel

A subset of our speakers will briefly introduce their career paths and answer questions about their career trajectories in academia.  Related questions on finding collaborations, applying for jobs, and work-life balance are welcome.  This event should be especially relevant to graduate students and postdocs.  One of the organizers will moderate this informal panel, and all are welcome.

Mixed norm decoupling for paraboloids (slides)

Zane Li (NCSU)

In this talk we discuss mixed norm decoupling estimates for the paraboloid. One motivation of considering such an estimate is a conjectured mixed norm Strichartz estimate on the torus which essentially is an estimate about exponential sums. This is joint work with Shival Dasu, Hongki Jung, and José Madrid.

Coffee break 10:30 - 11:00

Faithful induction theorems and the Chebotarev density theorem

Robert Lemke Oliver (Tufts University)

The Chebotarev density theorem is a powerful and ubiquitous tool in number theory used to guarantee the existence of infinitely many primes satisfying splitting conditions in a Galois extension of number fields. In many applications, however, it is necessary to know not just that there are many such primes in the limit, but to know that there are many such primes up to a given finite point. This is the domain of so-called effective Chebotarev density theorems. In forthcoming joint work with Alex Smith that extends previous joint work of the author with Thorner and Zaman and earlier work of Pierce, Turnage-Butterbaugh, and Wood, we prove that in any family of irreducible complex Artin representations, almost all are subject to a very strong effective prime number theorem. This implies that almost all number fields with a fixed Galois group are subject to a similarly strong effective form of the Chebotarev density theorem. Under the hood, the key result is a new theorem in the character theory of finite groups that is similar in spirit to classical work of Artin and Brauer on inductions of one-dimensional characters.

Closing and lunch 12:00