Dimitris Koukoulopoulos - Université de Montréal - Département de mathématiques et de statistique

I am a Professor at the Department of Mathematics and Statistics of the University of Montreal, and a member of the Montreal Number Theory Group. I work in analytic number theory with a focus on multiplicative and probabilistic aspects of number theory, the anatomy of integers and permutations, sieve methods, and additive combinatorics.

Prospective students: I am looking for strong M.Sc. and Ph.D. students. Please take a look at my list of publications and, if you think our research interests overlap, send me an e-mail and submit an application.

### 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

#### Employment

• 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

### Research funding

#### 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, M. Lalín, M. Radziwill), 2018-21, $162,000 • Établissement de nouveaux chercheurs universitaires, 2012-14,$40,000

### Service

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

### Supervision

#### Doctoral students

• 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)
• Joëlle Matte (M.Sc. 2018)
• Peter Zenz (M.Sc. 2017, joint with E. Kowalski, M. Radziwill)
• Antoine Comeau-Lapointe (M.Sc. 2016)

 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

### 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

### 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

### 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.

### E-mail

dimitris.koukoulopoulos@umontreal.ca

### Office

Address: Université de Montréal, 2920 chemin de la Tour, Pavillon André Aisenstadt, Bureau 4163
Phone: +1 (514) 343-6716

Université de Montréal
CP 6128, Succ. Centre-Ville

Université de Montréal
2920 chemin de la Tour