SCIENTIFIC PROGRAMS AND ACTIVITIES

April 25, 2014

June 30-July 11, 2008
Summer School in Analytic Number Theory and Diophantine Approximation
University of Ottawa, Ontario Canada

Organizing Commitee: Nathan Ng, Damien Roy
Scientific Commitee: Nathan Ng, Damien Roy, Kannan Soundararajan

Registration
on site June 30
Fees: $50 graduate students /week.
Postdocs and researchers without grants $75 /week.
For all others $100/week.

Schedule of Summer School

Scientific Material for Summer School

Pictures from the Summer School

Participant List
Accommodation and Travel to Ottawa
Speakers

Summer School Overview

The primary objective of this summer school is to give young mathematicians an opportunity to learn the latest methods and results in analytic number theory and Diophantine approximation. In the first week, several introductory courses will be offered in order to give some background for beginning graduate students. The second week will have more advanced courses with some of the more recent developments in each field.

The fields of analytic number theory and Diophantine approximation have undergone considerable progress in the last ten years. In these respective fields, there have been important results proven by Goldston, Pintz, and Yildirim on small gaps between primes and by Rivoal and others on the irrationality of the odd values of the zeta function. This summer school will expose the participants to key ideas and tools behind some of these achievements.

Another objective is to expose young mathematicians who are working in one of these fields to the ideas and techniques of the other one. This meeting will allow for interactions between researchers who work on very different problems. This could prove to be a great benefit for the participants. Recent years have seen many ingenious results that combine techniques from several different areas of mathematics. It often occurs that seemingly difficult problems in one field can be more simply understood by the methods and language of another field of mathematics.

This summer school is affiliated to the tenth conference of the Canadian Number Theory Association (CNTA X) which will take place from July 13 to July 18, 2008 in Waterloo, Ontario. It is one of the largest international conferences specializing in number theory. By holding this school just before CNTA X, the students will have an opportunity to learn background material for 2 weeks and then attend the Waterloo meeting. This could prove to be an excellent way for students to learn new ideas, to find research problems, and to interact with many of the leading experts in number theory.

Speakers

Francesco Amoroso, Université de Caen
Andrew Granville, Université de Montréal
Nathan Ng, University of Ottawa
Damien Roy, University of Ottawa
Kannan Soundararajan, Stanford University
Michel Waldschmidt, Université Pierre et Marie Curie (Paris VI)

Schedule:

Each day will consist of three lectures of 1h20 in the lecture room MNT 203 of Montpetit Hall.
Montpetit Hall on the campus map http://www.uottawa.ca/cartes/campus-principal.html

Participants are asked to pick their registration kit on Monday June 30 at 8:30 in room MNT 207, prior to the first lecture. Coffee will also be served at 8:30 on this occasion.

There will be lectures on July 1 (Canada day) as well. Talks will begin the morning of June 30 and end midday on July 11.

First Week
Jun 30-Jul 4

For the first week, the first lecture of each day will be given by Michel Waldschmidt, followed by the lectures of Nathan Ng and Damien Roy.

First lecture: 9:00 to 10:20, room MNT 203

Lectures by Michel Waldschmidt:

  • Irrationality of some constants coming from analysis.
  • Historical introduction to transcendence methods: Hermite, Padé's
    approximants.
  • Interpolation series and Polya's theorem, Gel'fond's proof of the transcendence of e^pi; Gramain's theorem.
  • R. Lagrange's interpolation following T. Rivoal.
  • Hilbert's seventh problem, Dirichlet box principle, Thue-Siegel lemma, auxiliary functions, extrapolation.
  • Interpolation determinants of M. Laurent, proof of Polya's theorem.
Coffee break: 10:20 to 10:40, room MNT 207
(The "coffee" room MNT 207 will be open from 8:00 to 17:00 each day from June 30 to July 11, including the week-end in case some of you want to work there. )

JULY 1 Schedule

8:00- 9:20: lecture by Michel Waldschmit
9:30-10:50: lecture by Nathan Ng
10:50-11:10: break
11:10-12:30: lecture by Damien Roy

Afternoon Free

Second lecture: 10:40 to 12:00, room MNT 203

Lectures by Nathan Ng:

  • The distribution of prime numbers.
  • Gaps between primes.
  • Primes in arithmetic progressions.
  • Sieve methods.
  • Riemann zeta function, L-functions
Lunch: 12:00 to 14:00

Third lecture: 14:00 to 15:20, room MNT 203

Lectures by Damien Roy:

  • Zero estimates.
  • Criteria of algebraic independence.
  • Applications.
Second week
Jul 7-11

In the second week, the first lecture of the day will be given by Kannan Soundararajan, followed by those of Francesco Amoroso and Andrew Granville.

First lecture:
9:00 to 10:20, room MNT 203

Kannan Soundararajan:

  • Distribution of values of L-functions.
  • Vanishing and non-vanishing of L-functions.
  • Mean values estimates

 

Coffee break: 10:20 to 10:40, room MNT 207
(The "coffee" room MNT 207 will be open from 8:00 to 17:00 each day from June 30 to July 11, including the week-end in case some of you want to work there. )
Second lecture: 10:40 to 12:00, room MNT 203

Francesco Amoroso:

  • Mahler's measure and heights of algebraic numbers, theorems of Northcott and Kronecker, Lehmer's problem and Dobrowolski's theorem.
  • Valuations on a number field ,Weil's height and the product formula, sketch of the proof of Dobrowolski's theorem.
  • Some geometry on tori (subgroups, degrees, ...), some commutative algebra, bounds for the Hilbert function. Bogomolov's problem and Lehmer's problem's on tori: recent results.
  • A sketch of the proof of a sharp Bogomolov's bound.
  • A sketch of the proof of a sharp Lehmer's bound.
Lunch: 12:00 to 14:00
Third lecture: 14:00 to 15:20, room MNT 203

Andrew Granville:

  • The uncertainty principle.
  • Bounds for characters sums.
  • Mean values of multiplicative functions

Special events:

"Monday June 30: dinner at the Jazzy Restaurant (University Centre, Jock Turcot Hall) from 18:00 to 20:00.
" Monday July 7: lunch at the Jazzy Restaurant from 12:00 to 14:00.
" Wednesday July 9: dinner at the Jazzy Restaurant from 18:00 to 20:00.

Computer facilities:

  • Participants will have access to the computer lab in room MNT 140 to check email. You must present yourself to the computer help desk and show your badge in order to have access to a computer. You may also have to wait for a computer to be available. Lab hours are Monday to Friday from 8:30 to 20:00, and 13:00 to 17:00 on weekends.
  • For those who come with portable computers, a limited number of accounts has been created for wi-fi access. Please ask for an account at the time of registration.

Library:

The Science Library is located in Morisset Hall. Monographs can be found on the third floor and periodicals on the sixth floor.

Residences:

If you reserved a room in the Stanton Residences or an apartment in the New Residences, you should go at your arrival to the registration desk of the residences located at 90 University to receive your keys.

** For those who reserved an apartment in the New Residences, you need to bring with you utensils and plates (and maybe a little bit of detergent to clean them), as nothing is furnished besides sheets and towels. **

Accomodations in Ottawa.

Facilities and locations

The department of Mathematics and Statistics is in 585 King Edward Ave, opposite Fauteux Hall. The library of the University is in Morisset building (MRT). The monographs in mathematics are located on the third floor and the periodicals on the sixth floor.

There are many dining possibilities on or near the campus: the cafeteria in Jock Turcot Centre; the Nostalgica,graduate student pub across from Thomson residence; the Zoompub in the Sports Complex and several small restaurants, eateries and pubs on Laurier, Osgoode, and Somerset Streets, just off campus.

Funding Support for current graduate students

Funding to support graduate students to the Summer School has been made possible by support from the Fields Institute and the National Science Foundation. Deadline to apply for support April 1, 2008. Applicants are requested to fill the application form in order to be considered for financial support.

Affiliated Activities:

* Tenth conference of the Canadian Number Theory Association (CNTA X) : July 13th to 18th, 2008, Waterloo, Ontario. It is possible to apply for funding until June 1. More details are available on the web page of the conference:
http://www.fields.utoronto.ca/programs/scientific/08-09/CNTAX/

* Fields Institute Workshop on New Directions in Cryptography: June 25th to 27th, 2008, University of Ottawa. Details are available at
http://www.fields.utoronto.ca/programs/scientific/07-08/cryptography/

Participant List

Fullname University Name Week 1 Week 2
Akhtari, Shabnam University of British Columbia 1 1
Amoroso, Francesco Université de Caen 1 1
An, Wenyong University of Waterloo 1 1
Anwar, Muhammad Fazeel University of York 1 1
Baczkowski, Daniel University of South Carolina 1 1
Badziahin, Dzmitry University of York 1 1
Bardestani, Mohammad Université de Montréal 1 1
Bel, Pierre Université Bordeaux 1 1 1
Bell, Jordan University of Toronto 1 1
Benzaoui, Ilhem USTHB (Algeria) 1 1
Bober, Jonathan University of Michigan 1 1
Butler, Lee University of Bristol 1 1
Buttcane, Jack University of California, Los Angeles 1 1
Caley, Timothy University of Waterloo 1 1
Chadozeau, Arnaud Université de Montréal 1 1
Chandee, Vorrapan Stanford University 1 1
Chen, Huei Jeng National Central University 1 1
Chuang, Chih-Yun National Tsing Hua University 1 1
Coons, Michael Simon Fraser University 1 1
de Crisenoy, Marc University of La Reunion 1 1
Delsinne, Emmanuel Université de Caen 0 1
Droll, Andrew Queen's University 1 0
El basraoui, Abdelkrim University of Ottawa 1 0
Ernvall-Hytönen, Anne-Maria University of Turku 1 1
Fiorilli, Daniel Université de Montréal 1 1
Goldmakher, Leo Stanford University 1 1
Granville, Andrew Université de Montréal 1 1
Guedes, Gabriel Universidade Federal de Minas Gerais 1 0
Gun, Sanoli Queen's University 1 1
Hambrook, Kyle University of Lethbridge 1 0
Harvey, Michael University of Bristol 1 1
Henriot, Kevin ENS Lyon 1 1
Homma, Kosuke University of Texas at Austin 0 1
Horwood, Geneviève University of Ottawa 1 1
Hough, Robert Stanford University 1 1
Huang, Jingjing Pennsylvania State University 0 1
Hughes, Kevin Princeton University 1 1
Hulin, Jerome Laboratoire d'Informatique Fondamentale 1 1
Hussain, Mumtaz University of York 1 1
Jurvanen, Henna University of Joensuu 1 1
Justus, Benjamin Concordia University 1 0
Kadiri, Habiba University of Lethbridge 0 1
Karimianpour, Camelia University of Ottawa 1 0
Kleinman, Aaron University of California, Berkeley 1 1
Kovács, Tünde University of Debrecen 1 1
Kristensen, Simon University of Aarhus 1 1
Laishram, Shanta University of Waterloo 1 1
Lamzouri, Youness Université de Montréal 0 1
Le, Thai Hoang University of California, Los Angeles 1 1
Leahy, James-Michael McGill University 1 1
Lev, Vsevolod University of Haifa at Oranim 1 1
Li, Xiannan Stanford University 1 1
Loughran, Daniel University of Bristol 1 1
Lozier, Stéphane University of Ottawa 1 1
Maillot, François École Normale Supérieure 1 1
Martel, Justin Harry University of Ottawa 1 1
Masuda, Ariane University of Ottawa 1 0
Meier, Peter University of Wuerzburg 1 1
Merilä, Ville University of Oulu 1 1
Morris, Dave University of Lethbridge 1 1
Murty, Ram Queen's University 1 0
Ng, Nathan University of Lethbridge 1 1
Nguyen, Hoi Rutgers University 1 1
O'Shea, Donal Mount Holyoke College 1 0
Pejkovic, Tomislav University of Zagreb 1 1
Pontreau, Corentin Université de Caen 1 1
Radziwill, Maksym McGill University 1 1
Rath, Purusottam Queen's University 1 0
Rishikesh, R. University of Waterloo 0 1
Roy, Damien University of Ottawa 1 1
Rundle, Robert Queen's University 1 1
Sitar, Scott University of British Columbia 1 1
Soundararajan, Kannan Stanford University 1 1
Spencer, Craig University of Michigan 1 1
Steuding, Rasa   1 1
Sutantyo, Daniel Macquarie University 1 1
Taylor, Karen University of Nottingham 1 1
Thom, Mark University of Lethbridge 1 1
Tu, Fang-Ting National Chiao Tung University 1 1
Virtanen, Henri University of Turku 1 1
Waldschmidt, Michel Université Paris VI 1 1
Weatherby, Chester Queen's University 1 1
Weiss, Benjamin University of Michigan 1 1
Wigman, Igor Université de Montréal 1 1
Wright, Thomas Johns Hopkins University 1 1
Yagoub, Hemza University of Ottawa 1 0
Yusupova, Tatiana University of York 1 1
Zelo, Dmitrij University of Ottawa 1 1
Zhao, Xiaomei University of Waterloo 1 1
Zywina, David University of Pennsylvania 1 1

 

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