Biographical Information

Education

• Ph.D. in mathematics, University of Illinois at Urbana-Champaign, 2010
• Master's in mathematics, University of Illinois at Urbana-Champaign, 2007
• Undegraduate degree in mathematics, Aristotle University of Thessaloniki, 2006

Main academic positions

• Chaire Courtois II in fundamental mathematics, Université de Montréal, 2021-28
• Professor, Université de Montréal, 2021-
• Associate Professor, Université de Montréal, 2017-21
• Assistant Professor, Université de Montréal, 2012-17
• CRM-ISM Postdoctoral Fellow, Centre de recherches mathématiques, Montreal, 2010-12

Other affiliations

• Regular member, Centre de recherches mathématiques, Montreal, 2013-
• Adjunct Professor, McGill University, 2017-
• Research member, Institut Mittag-Leffler, Stockholm, Feb-Mar 2021
• Visiting Professor, University of Genova, June 2019
• Visiting Professor, University of Oxford, Jan-May 2019
• Research member, Mathematical Sciences Research Institute, Berkeley, CA, Jan-May 2017

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Research funding

Fondation Courtois

• Chaire Courtois II in fundamental mathematics, 2021-28, $700,000

Natural Sciences and Engineering Research Council of Canada

• Discovery Grant, 2018-23, $140,000
• Discovery Grant, 2013-18, $100,000

Fonds de Recherche du Québec - Nature et Technologies

• Projet de recherche en équippe (with C. David, A. Granville, M. Lalín), 2021-24, $150,000
• Projet de recherche en équippe (with C. David, M. Lalín, M. Radziwill), 2018-21, $162,000
• Établissement de nouveaux chercheurs universitaires, 2012-14, $40,000

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Distinctions

• Top 10 scientific discoveries of 2020 (joint with J. Maynard), Québec Science Magazine
• P. R. Halmos - L. R. Ford Award (joint with J. Thiel), 2013, Mathematical Association of America

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Supervision

Doctoral students

• Tony Haddad (current)
• Arghya Datta (current, joint with A. Granville)
• Stelios Sachpazis (current)
• Peter Zenz (current, joint with M. Radziwill)
• Kunjakanan Nath (current)
• Crystel Bujold (Ph.D. 2020, joint with A. Granville)
• Marzieh Mehdizadeh (Ph.D. 2017, joint with A. Granville)

Master's students

• Jonah Klein (current)
• Simon Lemieux (current)
• Tony Haddad (M.Sc. 2020)
• Joëlle Matte (M.Sc. 2018)
• Peter Zenz (M.Sc. 2017, joint with E. Kowalski, M. Radziwill)
• Antoine Comeau-Lapointe (M.Sc. 2016)

Summer undergraduate students

• 2020: Jonah Klein, Simon Lemieux
• 2016: Antoine Giard, Youcef Mokrani
• 2015: Mathieu Nassif, Fabrice Nonez
• 2013: Vincent Girard (joint with M. Lalín), Manuela Piñeros-Rodriguez (joint with M. Hamel)
• 2012: Patrick Da Silva, Suryateja Gavva, Olivier Martin (all joint with A. Granville)
• 2011: Philippe Charron

Postdoctoral fellows (all co-supervised)

• George Shakan, 2021-
• Alyssa Lumley, 2019-
• Sacha Mangerel, 2018-
• Aled Walker, 2019-20
• Cathy Swaenepoel, 2019-20
• Corentin Perret-Gentil, 2017-19
• Niko Laaksonen, 2017-18
• Xianchang Meng, 2017-18
• Mattia Righetti, 2016-18
• Stephen Lester, 2016-17
• Sumit Giri, 2015-16
• Alastair Irving, 2014-15
• Marc Munsch, 2014-15

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Selected invited lectures

Conferences

• Plenary speaker, Journées Arithmétiques, 2022, Nancy, France
• Plenary speaker, Number Theory Down Under, 2021, Sidney, Australia
• Erdős Lecture Series, 2020, University of Memphis
• Second Symposium on Analytic Number Theory, 2019, Cetraro, Italy
• Pomerance 71, 2015, Athens, GA
• Analytic Number Theory, 2014, Clay Mathematics Institute, Oxford
• Fouvry 60, 2013, CIRM, Luminy, France
• Canadian Number Theory Association XII Meeting, 2012, Lethbridge

Lecture series

• École Langlands (postponed due to COVID-19), CRM, Montreal
• Workshop on the Duffin-Schaeffer conjecture, 2019, Heilbronn Institute, Bristol, UK
• 2nd French-German Summer School, 2019, Dresden, Germany
• Summer School Gaps between Primes and Analytic Number Theory, 2015, MSRI, Berkeley

Colloquia

• University of Waterloo, 2020
• Queen's University, 2020
• University of Illinois at Urbana-Champaign, 2019
• Princeton University, 2019
• Stony Brook University, 2019
• CRM, Montreal, 2014

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Service

• Director of Graduate Studies in mathematics, Université de Montréal, 2019-21
• Scientific Committee, 2020 Winter Meeting of the Canadian Mathematical Society
• Co-organizer, Workshop Probability in Number Theory, CRM, Montreal, 2018
• Co-organizer, Colloque des sciences mathématiques du Québec, CRM, Montreal, 2016-18

Research papers

1. Irreducibility of random polynomials: general measures (with L. Bary-Soroker and G. Kozma).
   Preprint, 64 pages, submitted for publication.
2. Equal sums in random sets and the concentration of divisors (with K. Ford and B. Green).
   Preprint, 88 pages, submitted for publication.
3. A note on the natural density of product sets (with S. Bettin and C. Sanna).
   Bull. London Math. Soc., 6 pages, to appear.
4. Sieve weights and their smoothings (with A. Granville and J. Maynard).
   Ann. Sci. Éc. Norm. Supér., 85 pages, to appear.
5. On the Duffin-Schaeffer conjecture (with J. Maynard).
   Ann. of Math., 192 (2020), 251-307. DOI: 10.4007/annals.2020.192.1.5
6. The structure of multiplicative functions with small partial sums (with K. Soundararajan).
   Discrete Anal., 2020:6, 19 pp. DOI: 10.19086/da.11963
7. Beyond the LSD method for the partial sums of multiplicative functions (with A. Granville).
   Ramanujan J. 49 (2019), no. 2, 287-319. DOI: 10.1007/s11139-018-0119-3
8. The frequency and the structure of large character sums (with J. Bober, L. Goldmakher and A. Granville).
   J. Eur. Math. Soc. (JEMS) 20 (2018), no. 7, 1759-1818. DOI: 10.4171/JEMS/799
9. Sums of Euler products and statistics of elliptic curves (with C. David and E. Smith).
   Math. Ann., 368 (2017), 685-752. DOI: 10.1007/s00208-016-1482-2
10. Permutations contained in transitive subgroups (with S. Eberhard and K. Ford).
    Discrete Anal., 2016:12, 34 pp. DOI: 10.19086/ da.849
11. The frequency of elliptic curve groups over prime finite fields (with V. Chandee, C. David and E. Smith).
    Canad. J. Math, 68 (2016), no. 4, 721-761. DOI: 10.4153/CJM-2015-013-1
12. Best possible densities, as a consequence of Zhang- Maynard-Tao (with A. Granville, D. M. Kane and R. Lemke Oliver).
    Analytic number theory. In honor of Helmut Maier's 60th birthday. pp. 133-144, Springer, Cham, 2015.
13. Primes in short arithmetic progressions.
    Int. J. Number Theory, 11 (2015), no. 5, 1499-1521. DOI: 10.1142/S1793042115400035
14. When the sieve works (with A. Granville and K. Matomäki).
    Duke Math. J., 164 (2015), no. 10, 1935-1969. DOI: 10.4064/aa162-3-2
15. On the concentration of certain additive functions.
    Acta Arith., 162 (2014), no. 3, 223-241. DOI: 10.4064/aa162-3-2
16. On the number of integers in a generalized multiplication table.
    J. Reine Angew. Math., 689 (2014), 33-99. DOI: 10.1515/crelle-2012-0064
17. Group structures of elliptic curves over finite fields (with V. Chandee, C. David and E. Smith).
    Int. Math. Res. Not. IMRN, 2013, 15 pages. DOI: 10.1093/imrn/rnt120
18. On multiplicative functions which are small on average.
    Geom. Funct. Anal., 23 (2013), no. 5, 1569-1630. DOI: 10.1007/s00039-013-0235-6
19. Pretentious multiplicative functions and the prime number theorem for arithmetic progressions.
    Compos. Math., 149 (2013), no. 7, 1129-1149. DOI: 10.1112/S0010437X12000802
20. Divisors of shifted primes.
    Int. Math. Res. Not. IMRN, 2010, no. 24, 4585-4627. DOI: 10.1093/imrn/rnq045
21. Localized factorizations of integers.
    Proc. London Math. Soc. (3), 101 (2010), no. 2, 392-426. DOI: 10.1112/plms/pdp056
22. A reciprocity theorem for certain hypergeometric series (with B. C. Berndt).
    Proc. Amer. Math. Soc., 137 (2009), 2369-2373. DOI: 10.1090/S0002-9939-09-09777-9

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Books

The Distribution of Prime Numbers, Graduate Studies in Mathematics, 203. American Mathematical Society, Providence, RI, 2019.

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Expository papers

Arrangements of stars on the American flag (with J. Thiel).
Amer. Math. Monthly, 119 (2012), no. 6, 443-450. DOI: 10.4169/amer.math.monthly.119.06.443

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Ph.D. Thesis

Generalized and restricted multiplication tables of integers. Thesis (Ph.D.)-University of Illinois at Urbana-Champaign. 2010.

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Course notes

• 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.

• Théorie des nombres (in French): these notes were written for an advanced undergraduate course in Number Theory. The contents include basic elementary number theory, a brief introduction to group theory and its applications to the study of modular arithmetic, an introduction to diophantine equations, and an introduction to Analytic Number Theory.

• Algèbre 2 (in French): these are the notes for the second part of an undergraduate course in Abstract Algebra. They cover basic ring and module theory.

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Slides

• Sieve weights and their smoothings, Analytic Number Theory, Oberwolfach, November 10, 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.

Updates on my research and other news

• As of June 2021, and for seven years, I will hold the Chaire Courtois II in fundamental mathematics.
• New paper by Stelios Sachpazis on values of multiplicative functions at consecutive integers.
• My work with James Maynard on the Duffin-Schaeffer conjecture was selected among the top 10 scientific discoveries of 2020 of the Québec Science Magazine
• New paper with Lior Bary-Soroker and Gady Kozma. Among other things, we prove that if \(f\) is a randomly selected monic polynomial with coefficients in \(\{0,1\}\) and of degree \(n\to\infty\), it is irreducible with probability \(\ge1/1000\). In addition, we prove that the probability becomes \(\sim1\) when the coefficients are drawn from \(\{1,\dots,H\}\) with \(H\ge35\).
• Kunjakanan Nath won the 2020 Serge-Bissonnette prize, awarded annually to a math grad student of the University of Montreal.
• My book The Distribution of Primes Numbers is now available at the AMS bookstore and at Amazon.
• General audience articles explaining the Duffin-Schaeffer conjecture published by Scientific American, Quanta Magazine and UdeM nouvelles (in French).

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Upcoming talks and travel

• London Number Theory Seminar, May 5, 2021
• CMS 2021 summer meeting, June 10, 2021
• Greek Mathematical Seminar, June 16, 2021
• Mathematical Congress of Americas, July 19-24, 2021
• Number Theory Down Under, September 2021
• Number Theory Meeting - Torino
• Number Theory Web Seminar, October 28, 2021
• Journées Arithmétiques, Summer 2022 (TBD)