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

• Courtois Chair II in fundamental research, 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-
• Visiting Professor, Courant Institute, New York University, Nov-Dec 2021
• 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

• Courtois Chair II in fundamental research, 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

• Invited speaker, International Congress of Mathematicians, 2022, online (video of talk)
• 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 (ongoing)
• Stelios Sachpazis (ongoing)
• Peter Zenz (joint with M. Radziwill; Ph.D. 2022 → Postdocs at Brown and at Stanford)
• Kunjakanan Nath (Ph.D. 2021 → Postdoc at U. Illinois, Urbana-Champaign)
• Crystel Bujold (joint with A. Granville; Ph.D. 2020 → CEGEP teacher)
• Marzieh Mehdizadeh (joint with A. Granville; Ph.D. 2017 → Morgan Stanley, Montreal)

Master's students

• Jonah Klein (ongoing)
• Simon Lemieux (ongoing)
• Gabriel Zlatkine (ongoing)
• Arghya Datta (joint with A. Granville; M.Sc. 2021 → Ph.D. student at U. Montréal)
• Tony Haddad (M.Sc. 2020 → Ph.D. student at U. Montréal)
• Joëlle Matte (M.Sc. 2018 → CEGEP teacher)
• Peter Zenz (joint with E. Kowalski, M. Radziwill; M.Sc. 2017 → Ph.D. student at McGill)
• Antoine Comeau-Lapointe (M.Sc. 2016 → Ph.D. student at Concordia)

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)

• Valeriya Kovaleva, 2022-
• George Shakan, 2021-22.
• Alyssa Lumley, 2019-22. Currently: Assistant Professor (teaching stream) at York University.
• Sacha Mangerel, 2018-21. Currently: Assistant Professor at Durham University.
• Aled Walker, 2019-20. Currently: Lecturer at King's College London.
• Cathy Swaenepoel, 2019-20. Currently: Maître de conférences at Paris (Jussieu).
• Corentin Perret-Gentil, 2017-19. Currently: Machine learning scientist at Daedalean AG.
• Niko Laaksonen, 2017-18. Currently: Postdoc at Rényi Institute, Budapest.
• Xianchang Meng, 2017-18. Currently: Professor, Shandong University, China.
• Mattia Righetti, 2016-18. Currently: Researcher at U Genova
• Stephen Lester, 2016-17. Currently: Lecturer at King's College
• Sumit Giri, 2015-16. Currently: Assistant Professor at IIT Tirupati
• Alastair Irving, 2014-15
• Marc Munsch, 2014-15. Currently: Research Assistant Professor at U Genova.

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Selected invited lectures

Conferences

• Plenary speaker, Journées Arithmétiques, 2023, Nancy, France
• International Congress of Mathematicians, 2022, online (video of talk)
• Plenary speaker, Second Congress of Greek Mathematicians, 2022, Athens, Greece
• Plenary speaker, 2021 CMS Winter Meeting, online (video of talk)
• Plenary speaker, Number Theory Down Under, 2021, Sidney, Australia (video of talk)
• Erdős Lecture Series, 2020, University of Memphis

Lecture series

• École Langlands, 2021, 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

Departmental colloquia

• Aristotle University of Thessaloniki, 2020
• 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

• Number Theory Editor, European Journal of Mathematics, 2021-
• 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, 94 pages, submitted for publication.
3. A note on the natural density of product sets (with S. Bettin and C. Sanna).
   Bull. London Math. Soc., 53 (2021), no. 5, 1407-1413. DOI: 10.1112/blms.12506
4. Sieve weights and their smoothings (with A. Granville and J. Maynard).
   Ann. Sci. Éc. Norm. Supér., 54 (2021), no. 5, 1089-1177. DOI: 10.24033/asens.2478
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.
• Link to buy a hard copy or an e-copy from thepublisher
• Link to download a preliminary version of the book, made available with permission of the publisher

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Expository papers

1. Rational approximations of irrational numbers.
   Submitted to the Proceedings of the 2022 International Congress of Mathematicians.
2. 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

• Towards a high-dimensional theory of divisors of integers, Number Theory Web Seminar, October 2021.
• Rational approximations of irrational numbers, Number Theory Down Under, September 2021.
• Approximations de nombres irrationels par des nombres rationels, École Langlands, CRM, August 2021. [Lecture 1] [Lecture 2] [Lecture 3]
• Irreducibility of random polynomials of large degree, Greek Mathematical Seminar, June 2021.
• Sieve weights and their smoothings, Oberwolfach, November 2016.
• Permutations contained in transitive groups, Crete, May 2016.
• Sums of Euler products and statistics of elliptic curves, Pomerance 70, June 2015.
• Les écarts entre les nombres premiers, Club Mathématique, UdeM, April 2015.
• The frequency of elliptic curve groups over prime finite fields, CNTA XII, June 2014.
• Arrangements d'étoiles sur le drapeau américain, Club Mathématique, UdeM, April 2014.
• Pretentious multiplicative functions, CRM-ISM Colloquium, Montréal, March 2014.
• The distribution of the maximum of character sums, Fouvry 60, June 2013.
• Group structures of elliptic curves over finite fieds, 2012 CMS Winter Meeting, December 2012.
• When the sieve works, CNTA XII, June 2012.
• Generalized multiplication tables, QVNTS, October 2010.

Updates on my research and other news

• Peter Zenz will defend his Ph.D. thesis in the summer of 2022, and he will then join Brown University for a three year postdoc.
• New paper by Peter Zenz on the Quantum variance for holomorphic Hecke cusp forms on the vertical geodesic.
• New paper by Peter Zenz on a sharp bound for the fourth moment of holomorphic Hecke cusp forms.
• New paper by Kunjakanan Nath on primes with missing digits.
• Kunjakanan Nath defended his Ph.D. thesis in August 2021 and will be joining the University of Illinois at Urbana-Champaign for a three year postdoc.
• 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

• 2021 CMS Winter Meeting, December 2-7, 2021
• International Congress of Mathematicians, July 6-14, 2022
• Journées Arithmétiques, TBD