The Schedule PLANT
Schedule overview by day
Monday March 4: graduate pre-talks in the afternoon, reception
Tuesday March 5: 2 talks in the morning, lunch, 2 talks in the afternoon, conference dinner
Wednesday March 6: 2 talks in the morning, lunch, 1 talk in the afternoon followed by a career etc. panel
Thursday March 7: 2 talks in the morning, lunch
All events occur in Hall of the Arts (HOA) room 160, CMU campus
Day 1 - March 4 - Monday
Graduate-level pre-talks
Registration and Coffee outside HOA 160, 2:00-2:30
2:30 - 3:30
Fourier transform over integers modulo N and signal recovery
Speaker: Alex Iosevich (University of Rochester)
Imagine that we want to transmit a signal, given in the form of a sequence of s and s of length , and that we send this sequence after first encoding it as the discrete Fourier transform. Suppose that some of the Fourier coefficients are missing. Can we still recover the original signal? The answer turns out to be yes, and while many of the methods are elementary, this line of inquiry quickly leads to the heart of some very interesting problems in number theory, combinatorics, and harmonic analysis.
4:00 - 5:00
Hardy-Ramanujan circle method
Speaker: Amita Malik (Penn State)
The circle method invented more than a century ago by Hardy and Ramanujan to study integer partitions is still one of the most powerful tools in number theory. This method has been modified over the years, but the key-idea is pretty much the same. In this talk, we give an overview of this method and discuss some of its exciting applications.
Reception outside HOA 160, 5:00-6:30
Day 2 - March 5 - Tuesday
Main program begins, conference dinner
Registration 9:00-9:30
9:30 - 10:30
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
11:00 - 12:00
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
2:00 - 3:00
Benjamin Linowitz (Oberlin College)
The systole of a compact Riemannian manifold M is the least length of a non-contractible loop on M. In this talk I will survey some recent work with S. Lapan and J. Meyer on the systolic geometry of arithmetic locally symmetric spaces, emphasizing systole growth along congruence covers.
Coffee break 3:00 - 3:30
3:30 - 4:30
Lattice Covering Densities and Additive Combinatorics
Alexandria Rose (IAS)
Day 3 - March 6 - Wednesday
Main program including career panel
9:30 - 10:30
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
11:00 - 12:00
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
2:00 - 3:00
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
3:30 - 4:30
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.
Day 4 - March 7 - Thursday
Main program and conclusion
9:30 - 10:30
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
11:00 - 12:00
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