Workshop on Efficient Congruencing and Translation-invariant Systems

March 13 - 17, 2017, The Fields Institute

Location: Fields Institute, Room 230

Overview

This workshop will focus on the emerging area linking translation invariant Diophantine systems and mean values of exponential sums. In 2010, Wooley devised a new iterative approach to Vinogradov's method of estimating mean values of the one dimensional exponential sums ubiquitous in applications, thereby coming within a whisker of establishing the main conjectures in the subject. In this workshop, we will explore the latest developments in this area, with the goal of fostering interaction between experts of these methods with researchers from interfacing areas such as harmonic analysis, arithmetic geometry, and analytic number theorists in the broader sense.

Schedule

Monday, March 13th, 2017
09:20 to 09:30	Welcome / Opening Remarks
09:30 to 10:30	Efficient congruencing: the end of the beginning Trevor Wooley, University of Bristol
10:30 to 11:00	Coffee Break
11:00 to 12:00	Introduction to decoupling Larry Guth, Massachusetts Institute of Technology
12:00 to 14:00	Lunch
14:00 to 15:00	Short character sums modulo prime powers and applications: L-functions, primes, Kloosterman sums and the divisor function Igor Shparlinski, University of New South Wales
15:00 to 15:30	Coffee Break
15:30 to 16:00	Efficient uncongruencing Ana Zumalacárregui, University of New South Wales
16:10 to 17:10	Artin's conjecture in diophantine analysis Joerg Bruedern, Universitaet Goettingen
17:10 to 17:30	Discussions on Splinter Group Activities
17:30 to 19:00	Reception

Tuesday, March 14th, 2017
09:30 to 10:30	Decouplings and applications Ciprian Demeter, Indiana University
10:30 to 11:00	Coffee Break
11:00 to 11:30	Decoupling inequalities related to Parsell-Vinogradov systems in dimension two Shaoming Guo, Department of Mathematics
11:40 to 12:10	Vinogradov's mean value theorem in higher dimensions Scott Parsell, West Chester University
12:10 to 14:00	Lunch
14:00 to 16:30	Splinter Group Activities
16:30 to 17:00	Small zeros of congruences Rainer Dietmann, Royal Holloway, University of London

Wednesday, March 15th, 2017
09:30 to 10:30	The circle method in function fields Yu-Ru Liu, University of Waterloo
10:30 to 11:00	Coffee Break
11:00 to 11:30	Multidimensional Waring's problem in function fields Xiaomei Zhao, Central China Normal University
11:40 to 12:10	Effective Vinogradov's Mean Value Theorem Raphael Steiner, University of Bristol

Thursday, March 16th, 2017
09:00 to 10:00	Vinogradov's Mean Value and the Riemann Zeta-function Roger Heath-Brown, University of Oxford
10:00 to 10:30	Coffee Break
10:30 to 11:00	Vinogradov's mean value theorem in sieves with polynomial moduli and sieve applications Karin Halupczok, WWU Muenster
11:10 to 11:40	Combinatorial theorems in sparse arithmetic sets Sean Prendiville, University of Manchester
11:45 to 14:00	Lunch
14:00 to 16:30	Splinter Group Activities
16:30 to 17:00	Fractional parts of polynomials Roger Baker, Brigham Young University

Friday, March 17th, 2017
09:30 to 10:00	Sums of powers of almost equal primes Angel Kumchev, Towson University
10:10 to 10:40	The Hasse Principle for systems of quadratic and cubic diagonal equations Julia Brandes, Chalmers/Univ of Gothenburg
10:40 to 11:10	Coffee Break
11:10 to 11:40	Density of Binary Forms Robert Vaughan, The Pennsylvania State University
11:50 to 12:20	Applications of Vinogradov's mean value theorems in arithmetic harmonic analysis Kevin Hughes, University of Bristol
12:20 to 14:00	Lunch
14:00 to 14:30	The circle method for non-diagonal systems Simon Rydin Myerson, University College London
14:40 to 15:10	Waring's problem and ergodic theorems Brian Cook, The Fields Institute
15:10 to 15:30	Wrap up and Farewells

Submit abstract

Invited speakers can submit abstracts here.

Invited Speakers

Name	Affiliation
Roger Baker	Brigham Young University
Julia Brandes	Chalmers/Univ of Gothenburg
Joerg Bruedern	Universitaet Goettingen
Brian Cook	The Fields Institute
Ciprian Demeter	Indiana University
Rainer Dietmann	Royal Holloway, University of London
Shaoming Guo	Department of Mathematics
Larry Guth	Massachusetts Institute of Technology
Karin Halupczok	WWU Muenster
Roger Heath-Brown	University of Oxford
Kevin Hughes	University of Bristol
Angel Kumchev	Towson University
Yu-Ru Liu	University of Waterloo
Scott Parsell	West Chester University
Sean Prendiville	University of Manchester
Simon Rydin Myerson	University College London
Igor Shparlinski	University of New South Wales
Raphael Steiner	University of Bristol
Robert Vaughan	The Pennsylvania State University
Trevor Wooley	University of Bristol
Xiaomei Zhao	Central China Normal University
Ana Zumalacárregui	University of New South Wales

Registered Participants

Name	Affiliation
Ghorbat Ahmed	Government
Shabnam Akhtari	University of Oregon
Elie Alhajjar	George Mason University
Sedunova Alisa	Goettingen University
Roger Baker	Brigham Young University
William Banks	University of Missouri
Kirsti Biggs	University of Bristol
Dante Bonolis	ETH Zürich
Simon Boyer	Institut Camille Jordan
Julia Brandes	Chalmers/Univ of Gothenburg
Joerg Bruedern	Universitaet Goettingen
Sam Chow	University of York
Derya Ciray	University of Konstanz
Brian Cook	The Fields Institute
Ciprian Demeter	Indiana University
Kevin Destagnol	Université Paris 7-Paris Diderot
Rainer Dietmann	Royal Holloway, University of London
Lara Du	University of Michigan
Bryan Eelhart	The Fields Institute
Ertan Elma	University of Waterloo
Craig Franze	The Ohio State University at Marion
John Friedlander	University of Toronto
Ayla Gafni	University of Rochester
Luca Ghidelli	University of Ottawa
Shaoming Guo	Department of Mathematics
Larry Guth	Massachusetts Institute of Technology
Karin Halupczok	WWU Muenster
Brandon Hanson	The Pennsylvania State University
Roger Heath-Brown	University of Oxford
Harald Helfgott	University of Göttingen
Florian Herzig	University of Toronto
Khodabakhsh Hessami Pilehrood	The Fields Institute
Tatiana Hessami Pilehrood	The Fields Institute
Kevin Hughes	University of Bristol
Kian Kayler	Toronto Metropolitan University
Bryce Kerr	University of New South Wales
Cheikh Khoule	Université Cheikh Anta Diop de Dakar
Lars Kühne	The Fields Institute
Angel Kumchev	Towson University
Wentang Kuo	University of Waterloo
Junxian Li	University of Illinois at Urbana-Champaign
Yu-Ru Liu	University of Waterloo
Alexander Mangerel	University of Toronto
Khadija Mbarki	Faculty of sciences of Monastir
Juan Manuel Menconi	Instituto de Investigaciones Matemáticas Luis A. Santaló (IMAS)-CONICET
Anton Mosunov	University of Waterloo
Khoa Nguyen	University of British Columbia
Matt Olechnowicz	University of Toronto
Abhishek Oswal	University of Toronto
Marcelo Paredes	Universidad de Buenos Aires
Scott Parsell	West Chester University
Sean Prendiville	University of Manchester
Simon Rydin Myerson	University College London
Damaris Schindler	Universiteit Utrecht
George Shakan	University of Illinois at Urbana Champaign
Igor Shparlinski	University of New South Wales
Raphael Steiner	University of Bristol
Cameron Stewart	University of Waterloo
Lola Thompson	Oberlin College
Ling-Sang Tse	University of Toronto
Jacob Tsimerman	University of Toronto
Akshaa Vatwani	University of Waterloo
Robert Vaughan	The Pennsylvania State University
Hong Wang	Massachusetts Institute of Technology
Trevor Wooley	University of Bristol
Stanley Xiao	University of Oxford
Ping Xi	Xi'an Jiaotong University
Shuntaro Yamagishi	Queen's University
Asif Zaman	University of Toronto
Ruixiang Zhang	Princeton University
Xiaomei Zhao	Central China Normal University
Ana Zumalacárregui	University of New South Wales
Sebastian ZUNIGA ALTERMAN	Université Paris VII