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

• 2022 Ribenboim Prize, Canadian Number Theory Association
• Frontiers of Science Award (joint with J. Maynard), 2023, International Congress of Basic Science, Beijing
• 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

• Sayan Dutta, starting in Jan 2025
• Jeremy Schlitt (ongoing)
• Tony Haddad (ongoing)
• Stelios Sachpazis (Ph.D. 2023 → Postdoc at University of Turku)
• 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

• Jalal Kassab (ongoing)
• Félix Houde, ALGANT program: Concordia (2023-24), Paris-Saclay (2024-25)
• Jonah Klein (M.Sc. 2023 → Ph.D. student at U. South Carolina)
• Simon Lemieux (M.Sc. 2023)
• 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

• 2024: Rebecca Abi Abdallah
• 2022: Félix Houde
• 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

Visiting students

• 2024: Néo Tardy, M1 internship, ENS Paris-Saclay
• 2023: Ilyes Belkacem, M1 internship, ENS Paris-Saclay
• 2023-24: Yuetong Zhao, visiting PhD student, China University of Mining and Technology

Postdoctoral fellows (all co-supervised)

• Rachid Caich, 2024-present
• Daodao Yang, 2023-present
• Alessandro Fazzari, 2023-present
• Valeriya Kovaleva, 2022-present
• George Shakan, 2021-22. Currently: private sector.
• 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: private sector.
• Xianchang Meng, 2017-18. Currently: Professor, Shandong University, China.
• Mattia Righetti, 2016-18.
• 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: Maître de conférences at Université Jean Monnet.

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Selected invited lectures

Conferences

• Talk for Frontiers of Science Award, International Congress of Basic Sciences, 2023, Beijing, China
• 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, online (video of talk)
• Erdős Lecture Series, 2020, University of Memphis
• Canadian Number Theory Association XV Meeting, 2018, Laval University, Québec, Canada
• Deshouillers 70, 2017, Kerala School of Mathematics, India
• Pomerance 71, 2015, University of Georgia, Athens, GA
• Analytic Number Theory, 2014, Clay Mathematics Institute, Oxford, UK
• Canadian Number Theory Association XIII Meeting, 2014, University of Ottawa, Canada
• Number Theory at Illinois, 2014, University of Illinois at Urbana-Champaign
• Fouvry 60, Centre international de Rencontres Math\'ematiques, 2013, Luminy, France
• Canadian Number Theory Association XII Meeting, 2012, University of Lethbridge

Lecture series

• Alpbach workshop, 2024, Böglerhof, Austria.
• National Technical University of Athens, Summer School on Number Theory and Cryptography, Athens, Greece
• 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

• University of Illinois at Urbana-Champaign, 2023
• 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, Transactions and Memoirs of the Amer. Math. Soc., 2023-27
• 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. T. Haddad and D. Koukoulopoulos
   On Arratia's coupling and the Dirichlet law for the factors of a random integer
   Preprint (2024), 36 pages.
2. D. Koukoulopoulos, J. Maynard and D. Yang
   An almost sharp quantitative version of the Duffin-Schaeffer conjecture
   Duke Math. J., to appear.
3. K. Ford, D. Koukoulopoulos and T. Tao
   A lower bound on the mean value of the Erdős-Hooley Delta function
   Proc. London Math. Soc., 129 (2024), no. 1, Paper No. e12618, 18 pp.
   DOI: 10.1112/plms.12618
4. J. Klein, D. Koukoulopoulos and S. Lemieux
   On the \(j\)-th smallest modulus of a covering system with distinct moduli
   Int. J. Number Theory 20 (2024), no. 2, 471-479. DOI: 10.1142/S1793042124500234
5. D. Koukoulopoulos and T. Tao
   An upper bound on the mean value of the Erdős-Hooley Delta function
   Proc. London Math. Soc. (3) 127 (2023), no. 6, 1865-1885. DOI: 10.1112/plms.12572
6. L. Bary-Soroker, D. Koukoulopoulos and G. Kozma
   Irreducibility of random polynomials: general measures
   Invent. Math., 233 (2023), no. 3, 1041-1120. DOI: 10.1007/s00222-023-01193-6
7. K. Ford, B. Green and D. Koukoulopoulos
   Equal sums in random sets and the concentration of divisors
   Invent. Math. 232 (2023), no. 3, 1027-1160. DOI: 10.1007/s00222-022-01177-y
8. S. Bettin, C. Sanna and D. Koukoulopoulos
   A note on the natural density of product sets
   Bull. London Math. Soc. 53 (2021), no. 5, 1407-1413. DOI: 10.1112/blms.12506
9. A. Granville, D. Koukoulopoulos and J. Maynard
   Sieve weights and their smoothings
   Ann. Sci. Éc. Norm. Supér. 54 (2021), no. 5, 1089-1177. DOI: 10.24033/asens.2478
10. D. Koukoulopoulos and J. Maynard
    On the Duffin-Schaeffer conjecture
    Ann. of Math. 192 (2020), 251-307. DOI: 10.4007/annals.2020.192.1.5
11. D. Koukoulopoulos and K. Soundararajan
    The structure of multiplicative functions with small partial sums
    Discrete Anal. 2020:6, 19 pp. DOI: 10.19086/da.11963
12. A. Granville and D. Koukoulopoulos
    Beyond the LSD method for the partial sums of multiplicative functions
    Ramanujan J. 49 (2019), no. 2, 287-319. DOI: 10.1007/s11139-018-0119-3
13. J. Bober, L. Goldmakher, A. Granville and D. Koukoulopoulos
    The frequency and the structure of large character sums
    J. Eur. Math. Soc. (JEMS) 20 (2018), no. 7, 1759-1818. DOI: 10.4171/JEMS/799
14. C. David, D. Koukoulopoulos and E. Smith
    Sums of Euler products and statistics of elliptic curves
    Math. Ann. 368 (2017), 685-752. DOI: 10.1007/s00208-016-1482-2
15. S. Eberhard, K. Ford and D. Koukoulopoulos
    Permutations contained in transitive subgroups
    Discrete Anal. 2016:12, 34 pp. DOI: 10.19086/da.849
16. V. Chandee, C. David, D. Koukoulopoulos and E. Smith
    The frequency of elliptic curve groups over prime finite fields
    Canad. J. Math 68 (2016), no. 4, 721-761. DOI: 10.4153/CJM-2015-013-1
17. A. Granville, D. M. Kane, D. Koukoulopoulos and R. Lemke Oliver
    Best possible densities, as a consequence of Zhang-Maynard-Tao
    Analytic number theory. In honor of Helmut Maier's 60th birthday. pp. 133-144, Springer, Cham, 2015. DOI: 10.1007/978-3-319-22240-0_10
18. D. Koukoulopoulos
    Primes in short arithmetic progressions.
    Int. J. Number Theory 11 (2015), no. 5, 1499-1521. DOI: 10.1142/S1793042115400035
19. A. Granville, D. Koukoulopoulos and K. Matomäki
    When the sieve works
    Duke Math. J. 164 (2015), no. 10, 1935-1969. DOI: 10.1215/00127094-3120891
20. D. Koukoulopoulos
    On the concentration of certain additive functions.
    Acta Arith. 162 (2014), no. 3, 223-241. DOI: 10.4064/aa162-3-2
21. D. Koukoulopoulos
    On the number of integers in a generalized multiplication table.
    J. Reine Angew. Math. 689 (2014), 33-99. DOI: 10.1515/crelle-2012-0064
22. V. Chandee, C. David, D. Koukoulopoulos and E. Smith
    Group structures of elliptic curves over finite fields
    Int. Math. Res. Not. IMRN 2014, no. 19, 5230-5248. DOI: 10.1093/imrn/rnt120
23. D. Koukoulopoulos
    On multiplicative functions which are small on average.
    Geom. Funct. Anal. 23 (2013), no. 5, 1569-1630. DOI: 10.1007/s00039-013-0235-6
24. D. Koukoulopoulos
    Pretentious multiplicative functions and the prime number theorem for arithmetic progressions.
    Compos. Math. 149 (2013), no. 7, 1129-1149. DOI: 10.1112/S0010437X12000802
25. D. Koukoulopoulos
    Divisors of shifted primes.
    Int. Math. Res. Not. IMRN 2010, no. 24, 4585-4627. DOI: 10.1093/imrn/rnq045
26. D. Koukoulopoulos
    Localized factorizations of integers.
    Proc. London Math. Soc. (3) 101 (2010), no. 2, 392-426. DOI: 10.1112/plms/pdp056
27. B. C. Berndt and D. Koukoulopoulos
    A reciprocity theorem for certain hypergeometric series
    Proc. Amer. Math. Soc. 137 (2009), 2369-2373. DOI: 10.1090/S0002-9939-09-09777-9

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Books

D. Koukoulopoulos, 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 the publisher
• Link to download a preliminary version of the book (available with permission of the publisher)

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Expository papers

1. D. Koukoulopoulos
   Rational approximations of irrational numbers
   Proc. Int. Cong. Math. 2022, Vol. 3, pp. 1894-1916. EMS Press, Berlin, 2023. DOI: 10.4171/icm2022/84
2. D. Koukoulopoulos and J. Thiel
   Arrangements of stars on the American flag
   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 multiplicative number theory and basic estimates for prime numbers, modular arithmetic, an introduction to diophantine equations, and an introduction to transcedental number theory and the theory of continued fractions.

• 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

• Metric Diophantine Approximation. Lecture 1: Khinchin's theorem and its limitations, Alpbach workshop, Alpbach, Austria, June 2024.
• Divisors, CNTA XVI, Toronto, June 2024.
• Rational approximations of irrational numbers, International Congress of Basic Sciences, Beijing, July 2023.
• The Erdős-Hooley Delta function, Journées Arithmétiques, Nancy, France, July 2023.
• 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.