SCIENTIFIC PROGRAMS AND ACTIVITIES

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

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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