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Schedule
2019
Monday, May 20th
8:30 AM

Arrival and check-in, coffee

conference participants

Bryant Hall Gallery, first floor

8:30 AM - 9:15 AM

9:15 AM

Opening Remarks

Melissa Hodge-Penn, University of Mississippi
James Reid, University of Mississippi

Bryant Hall 209

9:15 AM - 9:30 AM

Welcome Assistant Vice Chancellor for Research

9:30 AM

Lecture 1

Kannan Soundararajan

Bryant Hall 209

9:30 AM - 10:30 AM

Introduction to the rest of lectures + value distribution of L-functions away from critical line.

10:30 AM

Coffee

conference participants

Bryant Hall Gallery, first floor

10:30 AM - 2:30 PM

Coffee and light refreshments will be available in the gallery daily.

9:00- 9:30 am

10:30 - 11:00 am

2:00 - 2:30 pm

11:00 AM

Lecture 2

Kannan Soundararajan

Bryant Hall 209

11:00 AM - 12:00 PM

Selberg's central limit theorem and analogues in families of L-functions (typical size of values on critical line).

2:30 PM

Landau-Siegel zeros and their illusory consequences

Kyle Pratt, University of Illinois

Bryant Hall 209

2:30 PM - 3:30 PM

Updated time

Abstract: Researchers have tried for many years to eliminate the possibility of LandauSiegel zeros—certain exceptional counterexamples to the Generalized Riemann Hypothesis. Often one thinks of these zeros as being a severe nuisance, but there are many situations in which their existence allows one to prove spectacular, though illusory, results. I will review some of this history and some of these results. In the latter portion of the talk I will discuss recent work, joint with H. M. Bui and Alexandru Zaharescu, in which we show that the existence of Landau-Siegel zeros has implications for the behavior of Dirichlet L-functions at the central point.

4:00 PM

An effective Chebotarev density theorem for families of fields, with an application to class groups

Caroline Turnage-Butterbaugh, Carleton College

Bryant Hall 209

4:00 PM - 5:00 PM

This talk will present an effective Chebotarev theorem that holds for all but a possible zero-density subfamily of certain families of number fields of fixed degree. For certain families, this work is unconditional, and in other cases it is conditional on the strong Artin conjecture and certain conjectures on counting number fields. As an application, we obtain nontrivial average upper bounds on ℓ-torsion in the class groups of the families of fields.

Tuesday, May 21st
9:30 AM

Lecture 3

Kannan Soundararajan

Bryant Hall 209

9:30 AM - 10:30 AM

Continuation of Selberg's central limit theorem and analogues in families of L-functions (typical size of values on critical line).

11:00 AM

Lecture 4

Kannan Soundararajan

Bryant Hall 209

11:00 AM - 12:00 PM

Larger values of L-functions on critical line -- moments, conjectures.

2:30 PM

Moments of cubic L-functions over function fields

Alexandra Florea, Columbia University

Bryant Hall 209

2:30 PM - 3:30 PM

Abstract: I will talk about some recent work with Chantal David and Matilde Lalin about the mean value of L-functions associated to cubic characters over F_q[t] when q=1 (mod 3). I will explain how to obtain an asymptotic formula which relies on obtaining cancellation in averages of cubic Gauss sums over functions fields. I will also talk about the corresponding non-Kummer case when q=2 (mod 3) and I will explain why this setting is somewhat easier to handle than the Kummer case, which allows us to prove some better results.

4:00 PM

High moments of L-functions

Vorrapan Chandee, Kansas State University

Bryant Hall 209

4:00 PM - 5:00 PM

Abstract: Moments of L-functions on the critical line (Re(s) = 1/2) have been extensively studied due to numerous applications, for example, bounds for L-functions, information on zeros of L-functions, and connections to the generalized Riemann hypothesis. However, the current understanding of higher moments is very limited. In this talk, I will give an overview how we can achieve asymptotic and bounds for higher moments by enlarging the size of various families of L-functions and show some techniques that are involved.

7:00 PM

Banquet

conference participants

Gertrude C. Ford Ballroom, The Inn at Ole Miss

7:00 PM - 9:00 PM

Wednesday, May 22nd
9:30 AM

Lecture 5

Kannan Soundararajan

Bryant Hall 209

9:30 AM - 10:30 AM

Progress towards moment conjectures -- upper and lower bounds.

11:00 AM

Lecture 6

Kannan Soundararajan

Bryant Hall 209

11:00 AM - 12:00 PM

Continuation of Progress towards moment conjectures -- upper and lower bounds.

Thursday, May 23rd
9:30 AM

Lecture 7

Kannan Soundararajan

Bryant Hall 209

9:30 AM - 10:30 AM

Extreme values of L-functions.

11:00 AM

Lecture 8

Kannan Soundararajan

Bryant Hall 209

11:00 AM - 12:00 PM

Continuation of Extreme values of L-functions.

2:30 PM

Extension of a positivity trick and estimates involving L-functions at the edge of the critical strip

Xiannan Li, Kansas State University

Bryant Hall 209

2:30 PM - 3:30 PM

Updated schedule

Abstract: I will review an old trick, and relate this to some modern results involving estimates for L-functions at the edge of the critical strip. These will include a good bound for automorphic L-functions and Rankin-Selberg L-functions as well as estimates for primes which split completely in a number field.

4:00 PM

The Weyl bound for Dirichlet L-functions

Matthew P. Young, Texas A&M University

Bryant Hall 209

4:00 PM - 5:00 PM

Abstract: In the 1960's, Burgess proved a subconvexity bound for Dirichlet L-functions. However, the quality of this bound was not as strong, in terms of the conductor, as the classical Weyl bound for the Riemann zeta function. In a major breakthrough, Conrey and Iwaniec established the Weyl bound for quadratic Dirichlet L-functions. I will discuss recent work with Ian Petrow that generalizes the Conrey-Iwaniec bound for more general characters, in particular arbitrary characters of prime modulus.

Friday, May 24th
9:30 AM

Lecture 9

Kannan Soundararajan

Bryant Hall 209

9:30 AM - 10:30 AM

Fyodorov--Keating conjectures, connections with random multiplicative functions.

11:00 AM

Lecture 10

Kannan Soundararajan

Bryant Hall 209

11:00 AM - 12:00 PM

Continuation of Fyodorov--Keating conjectures, connections with random multiplicative functions.

2:30 PM

The variance of counts of squarefrees in short intervals

Brad Rodgers, Queen's University

Bryant Hall 209

2:30 PM - 3:30 PM

Abstract: Consider the number of squarefree integers in a randomly 
chosen short interval. In this talk we will discuss a method for 
computing the variance of such a count. The estimate we arrive at 
improves an old result of R.R. Hall and confirms a conjecture of Keating 
and Rudnick in a restricted range. This is joint work with Ofir 
Gorodetsky, Bingrong Huang, and Maksym Radziwill.

4:00 PM

Open Problem Session

Ayla Gafni, University of Mississippi

Bryant Hall 209

4:00 PM - 5:00 PM