Université de Montréal - Département de mathématiques et de statistique - Dimitris Koukoulopoulos
Sieve methods: these notes were written for a graduate course on sieve methods at Université de Montréal in the Fall of 2012. While writing them I consulted various sources, primarily Kevin Ford's online notes and the book Opera de cribro by Friedlander and Iwaniec.
UPDATE (March 2015): the notes have been updated to incorporate the recent developements on small and large between primes, as well as a pretentious proof of the Siegel-Walfisz theorem.
The distribution of prime numbers: these notes were written for an introductory course to Analytic Number Theory. The contents include basic summation techniques, elementary prime number theory, a brief introduction to sieve methods, the Prime Number Theorem for arithmetic progressions, Linnik's theorem, the Bombieri-Vinogradov theorem, results on bounded gaps between primes, and the analytic theory of L-functions.
Analyse 2 (in French): these notes were written for the second part of an undergraduate course in Real Analysis. The contents include the theory of Riemann integration, asymptotic techniques for the estimation of sums and integrals, series and sequences of functions, and an introduction to Fourier series.
- Sieve weights and their smoothings, 2016 CMS Summer Meeting, Special Session on Analytic Number Theory and Diophantine equations, University of Alberta, Edmonton, June 26, 2016.
- Permutations contained in transitive groups, 15th Panhellenic Conference of Mathematical Analysis, University of Crete, May 28, 2016.
- Sums of Euler products and statistics of elliptic curves, Elementary, analytic, and algorithmic number theory : Research inspired by the mathematics of Carl Pomerance, University of Georgia, June 10, 2015.
- Les écarts entre les nombres premiers, Club Mathématique, Université de Montréal, April 11, 2015.
- The frequency of elliptic curve groups over prime finite fields, Canadian Number Theory Association XII Meeting, Carleton University, June 20, 2014.
- Arrangements d'étoiles sur le drapeau américain, Club Mathématique, Université de Montréal, April 9, 2014.
- Pretentious multiplicative functions, CRM-ISM Colloquium, Montréal, March 14, 2014.
- Group structures of elliptic curves over finite fieds, 2012 CMS Winter Meeting, Special Session on Analytic Number Theory, Montréal, December 8, 2012.
- When the sieve works, Canadian Number Theory Association XII Meeting, University of Lethbridge, June 22, 2012.
- Generalized multiplication tables, Québec-Maine Number Theory Conference, October 3, 2010.