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Summer Graduate School

Gaps between Primes and Analytic Number Theory July 13, 2015 - July 24, 2015
Parent Program:
Location: MSRI: Simons Auditorium
Organizers Dimitris Koukoulopoulos (Université de Montréal), LEAD Emmanuel Kowalski (ETH Zurich), James Maynard (University of Oxford), Kannan Soundararajan (Stanford University)
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Description
These courses will give students a full overview of the results of Zhang and Maynard on gaps between primes, and will provide them will a clear understanding of the tools involved. This will make accessible a significant part of modern analytic number theory. The lecturers will also make sure to include, within their course, examples and discussions going further than is strictly required to understand the proofs of Zhang and Maynard, e.g., in the direction of automorphic forms and the Riemann Hypothesis over finite fields. Bibliography (PDF) Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Exercise 6 Exercise 7 Exercise 8 GroupPhoto For eligibility and how to apply, see the Summer Graduate Workshop homepage
Keywords and Mathematics Subject Classification (MSC)
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Schedule, Notes/Handouts & Videos
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Jul 13, 2015
Monday
08:45 AM - 09:00 AM
  MSRI Intro
09:00 AM - 10:00 AM
  Lecture
Dimitris Koukoulopoulos (Université de Montréal)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
Dimitris Koukoulopoulos (Université de Montréal)
11:30 AM - 12:30 PM
  Discussion, short talks
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Lecture
Kannan Soundararajan (Stanford University)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  Discussion/Problems
Jul 14, 2015
Tuesday
09:00 AM - 10:00 AM
  Lecture
Dimitris Koukoulopoulos (Université de Montréal)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
Kannan Soundararajan (Stanford University)
11:30 AM - 12:30 PM
  Discussion, short talks
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Lecture
Dimitris Koukoulopoulos (Université de Montréal)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  Discussion/Problems
Jul 15, 2015
Wednesday
09:00 AM - 10:00 AM
  Lecture
James Maynard (University of Oxford)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
Dimitris Koukoulopoulos (Université de Montréal)
11:30 AM - 12:30 PM
  Discussion, short talks
12:30 PM - 02:00 PM
  BBQ Lunch
02:00 PM - 03:00 PM
  Extra Lecture/Discussion
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  Discussion/Problems
Jul 16, 2015
Thursday
09:00 AM - 10:00 AM
  Lecture
Kannan Soundararajan (Stanford University)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
Dimitris Koukoulopoulos (Université de Montréal)
11:30 AM - 12:30 PM
  Discussion, short talks
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Extra Lecture/Discussion
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  Discussion/Problems
Jul 17, 2015
Friday
09:00 AM - 10:00 AM
  Lecture
James Maynard (University of Oxford)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
Kannan Soundararajan (Stanford University)
11:30 AM - 12:30 PM
  Discussion, short talks
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Lecture
Emmanuel Kowalski (ETH Zurich)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  Discussion/Problems
Jul 20, 2015
Monday
09:00 AM - 10:00 AM
  Lecture
James Maynard (University of Oxford)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
Kannan Soundararajan (Stanford University)
11:30 AM - 12:30 PM
  Discussion, short talks 
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Lecture: The transition to life as a faculty member: jobs, associations, and professional development
Francis Su (Harvey Mudd College)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  Discussion/Problems
Jul 21, 2015
Tuesday
09:00 AM - 10:00 AM
  Lecture
Emmanuel Kowalski (ETH Zurich)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
Kannan Soundararajan (Stanford University)
11:30 AM - 12:30 PM
  Discussion, short talks
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Extra Lecture/Discussion
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  Discussion/Problems
Jul 22, 2015
Wednesday
09:00 AM - 10:00 AM
  Lecture
Emmanuel Kowalski (ETH Zurich)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
James Maynard (University of Oxford)
11:30 AM - 12:30 PM
  Discussion, short talks
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Lecture
Emmanuel Kowalski (ETH Zurich)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  Discussion/Problems
Jul 23, 2015
Thursday
09:00 AM - 10:00 AM
  Lecture
James Maynard (University of Oxford)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
Emmanuel Kowalski (ETH Zurich)
11:30 AM - 12:30 PM
  Discussion, short talks
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Extra Lecture/Discussion
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  Discussion/Problems
Jul 24, 2015
Friday
09:00 AM - 10:00 AM
  Lecture
Emmanuel Kowalski (ETH Zurich)
10:00 AM - 10:30 AM
  Coffee
10:30 AM - 11:30 AM
  Lecture
James Maynard (University of Oxford)
11:30 AM - 12:30 PM
  Discussion, short talks
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Extra Lecture/Discussion
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:30 PM
  Discussion/Problems