William Verreault
I am a 2nd year PhD student and Vanier Scholar in the Department of Mathematics at the University of Toronto. My advisor is Ilia Binder. Previously, I did my undergraduate and master's studies at Université Laval under the supervision of Javad Mashreghi, with a project on function spaces and their applications.
My research is in analysis and probability. My research program aims to get a better understanding of lattice models in statistical physics and their connections with complex analysis, function spaces, and random matrix theory. In particular, I am interested in SLE, the GFF, and GMC, and their interactions with random geometry and conformal field theory.
I am also an active member of the mathematical community, having notably served as Chair of the Student Committee of the Canadian Mathematical Society and as Student Director on its board. For more information about my involvement in academic life and mathematics outreach, see my CV. You will also find a list of my awards and teaching experience.
Publications
Submitted for publication
16. On the minimal length of addition chains. [PDF]
J.-M. De Koninck, N. Doyon, W. Verreault. 24 pp.
15. The Cesàro operator on local Dirichlet spaces. [arXiv, PDF]
E. Dellepiane, J. Mashreghi, M. Nasri, W. Verreault. 13 pp.
14. Moments of random multiplicative functions over function fields. [arXiv, PDF]
M. C. E. Hoffman, A. Hoganson, S. Menon, W. Verreault, A. Zaman. 32 pp.
13. Counting involutions on multicomplex spaces. [arXiv, PDF]
N. Doyon, P.-O. Parisé, W. Verreault. 23 pp.
12. A counterexample to symmetry of L^p norms of eigenfunctions. [arXiv, PDF]
G. Beiner, N. Eagles, W. Verreault, R. Wang. 6 pp.
11. Plank theorems and their applications: a survey. [arXiv, PDF]
W. Verreault. 46 pp.
Published/accepted
10. Arithmetic functions at factorial arguments. [arXiv, PDF]
J.-M. De Koninck, W. Verreault. Publ. Inst. Math. (2024), 115(129), 45-76.
9. Nonlinear expansions in reproducing kernel Hilbert spaces. [arXiv, PDF]
J. Mashreghi, W. Verreault. Sampl. Theory Signal Process. Data Anal. 21, 30 (2023), 17 pp.
8. On the tower factorization of integers. [arXiv, PDF]
J.-M. De Koninck, W. Verreault. Amer. Math. Monthly (2024), 8 pp.
7. Failure of L^p symmetry of zonal spherical harmonics. [arXiv, PDF]
G. Beiner, W. Verreault. J. Spectr. Theory (2023), no.1, 383-394.
6. A conjectural asymptotic formula for multiplicative chaos in number theory. [arXiv, PDF]
D. Aggarwal, U. Subedi, W. Verreault, A. Zaman, and C. Zheng. Res. Number Theory 8 (2022), no. 2, Paper No. 35, 19 pp.
5. Sums of random multiplicative functions over function fields with few irreducible factors. [arXiv, PDF]
D. Aggarwal, U. Subedi, W. Verreault, A. Zaman, C. Zheng. Math. Proc. Cambridge Philos. Soc. 173 (2022), no. 3, 715-726.
4. MacMahon partition analysis: a discrete approach to broken sticks problems. [arXiv, PDF]
W. Verreault. J. Combin. Theory Ser. A. 187 (2022): 105571, 15 pp.
3. On the probability of forming polygons from a broken stick. [arXiv, PDF]
W. Verreault. Statist. Probab. Lett. 180 (2022): 109237, 8 pp.
2. Repetitions of multinomial coefficients and a generalization of Singmaster’s conjecture. [arXiv, PDF]
J.-M. De Koninck, N. Doyon, W. Verreault. Integers 21 (2021), 11 pp.
1. Bounds for the counting function of the Jordan-Pólya numbers. [arXiv, PDF]
J.-M. De Koninck, N. Doyon, W. Verreault, A.A. Bonkli Razafindrasoanaivolala. Arch. Math. (Brno) 56 (2020), 141-152.
Expository articles and thesis
Développements en séries non linéaires. [PDF]
W. Verreault. Master thesis (2023).
Du triangle de Pascal aux simplexes de Pascal. [Accromath, PDF]
W. Verreault. Accromath, 15.2 (été-automne 2020), 18-23.
Talks and travels
Bold text below a bullet point indicates a talk title
Upcoming Travels
Complex Faces, in honor of Nikolai Makarov, Venice, Apr. 7 – 11
Ontario Graduate Mathematics Conference (OGMC), University of Toronto, May 30 – June 1
CMS Summer Meeting 2025, Université Laval, June 6 – June 9
PIMS-CRM Summer School in Probability, University of British Columbia, June 16 – June 27
2025
Number Theory Seminar, University of Waterloo, Mar. 7,
On the minimal length of addition chainsBird’s Eye Conference, University of Toronto, Mar. 1 – 2
The Gaussian free field for analystsWorkshop on Disordered Media, Rényi Institute, Jan. 27 – 31
School on Disordered Media, Rényi Institute, Jan. 20 – 24
Permanent of random Rademacher matricesJoint Mathematics Meetings (AMS Special Session on New Faces in Operator Theory), Seattle, Jan. 8 – 11,
The Cesàro operator on local Dirichlet spaces
2024
Probability Seminar, University of Victoria, Dec. 3,
Random multiplicative functions: past, present, and futureCMS Winter Meeting 2024 (Operator Theory, Function Theory, and Geometry: Connections to Corona Problems and Geometric Analysis), Kwantlen Polytechnic University, Nov. 29 – Dec. 2
The Cesàro operator on local Dirichlet spacesAnalysis and Applied Math Seminar, University of Toronto, Oct. 25,
The Cesàro operator on local Dirichlet spacesJunior Number Theory Seminar, University of Toronto, Oct. 24,
On the distribution of the minimal length of addition chainsGraduate Student Seminar, University of Toronto, Oct. 17,
Loops, Clusters, and WhatnotMidwest Probability Colloquium, Northwestern University, Oct. 10 – 12
Québec-Maine Number Theory Conference, Université Laval, Oct. 5 – 6,
Moments of random multiplicative functions over function fieldsAnalysis seminar, Université Laval, Oct. 4,
L'opérateur de Cesàro sur les espaces de Dirichlet locaux11th Heidelberg Laureate Forum (HLF), Heidelberg, Sept. 22 – 27
Visit Paris-Saclay University, Institut des Hautes Études Scientifiques and Institut de Mathématique d'Orsay, Sept. 16 – 20
Special topic school: ''Recent Developments in Disordered Systems'', Hausdorff Center for Mathematics, Sept. 9 – 13
Path Integrals and Friends Conference, University of Helsinki, Sept. 2 – 6
Advances in Probability Theory and Interacting Particle Systems: A Conference in Honor of S. R. Srinivasa Varadhan, Harvard University, Aug. 26 – 28
Forward From the Fields Medal, Fields Institute, Aug. 12 – 16
CMI-HIMR Summer School on Symmetry and Randomness, University of Bristol, July 15 – 19,
Schramm–Loewner evolution (SLE) in 2 minutes (Lightning talk)Workshop on Two-Dimensional Random Geometry, Institute for Mathematical and Statistical Innovation (IMSI), July 8 – 12
CRM-PIMS Summer School in Probability, Université de Montréal, July 1 – 5
Canadian Number Theory Association XVI (CNTA), Fields Institute, June 10 – 14
Ontario Graduate Mathematics Conference (OGMC), University of Waterloo, June 7 – 9,
Exploration of Lattice Models and SLECMS Summer Meeting 2024 (Number theory by early career researchers), University of Saskatchewan, May 31 – June 3,
Moments of random multiplicative functions over functions fieldsWorkshop III: Statistical Mechanics Beyond 2D (part of the Long Program on Geometry, Statistical Mechanics, and Integrability) Institute for Pure & Applied Mathematics (IPAM), May 6 – 10
Shapes and shades of Analysis: in depth and beyond / Formes et nuances de l’analyse moderne, Centre International de Rencontres Mathématiques (CIRM), Apr. 29 – May 3
Jane Street Graduate Research Fellowship Research Workshop, New York, Apr. 13 – 15,
Series expansion via unwinding (Poster)Bird’s Eye Conference, University of Toronto, Mar. 23 – 24,
Exploration of Lattice Models and SLEJunior Number Theory Seminar, University of Toronto, Mar. 19,
Probability and Number Theory ReduxWorkshop on New Directions in Conformal Field Theory, Fields Institute, Mar. 18 – 22
Universality & Integrability in KPZ Workshop, Columbia University, Mar. 11 – 15
Workshop on KPZ meets KPZ, Fields Institute, Mar. 4 – 8
Graduate Student Seminar, University of Toronto, Feb. 15,
Hypercomplex Analysis, Combinatorics, and Linear Algebra (Or how to count things in multicomplex spaces)Joint Mathematics Meetings (AMS Special Session on New Faces in Operator Theory and Function Theory), San Francisco, Jan. 3 – 6,
Nonlinear expansions in reproducing kernel Hilbert spaces
2023
CMS Winter Meeting 2023 (A celebration in honor of Jean-Marie De Koninck's 75th birthday: Elementary and Analytic Number Theory session), Montreal, Dec. 1 – 4,
Towers of primesAnalysis and Applied Math Seminar, University of Toronto, Nov. 17
Nonlinear expansions in reproducing kernel Hilbert spacesJunior Number Theory Seminar, University of Toronto, Nov. 1,
Probability and Number Theory10th Heidelberg Laureate Forum (HLF), Heidelberg, Sept. 24 – 29
Journées Arithmétiques, Université de Lorraine, July 3 – 7,
Sums of arithmetic functions running on factorialsCanadian Undergraduate Mathematics Conference (CUMC), University of Toronto, June 19 – 23,
Towers of primesEarly Career Research in Number Theory session (CMS Summer Meeting 2023), University of Ottawa, June 2 – 5,
Sums of arithmetic functions running on factorialsCMS Summer Meeting 2023 (Matrices and Operators session), University of Ottawa, June 2 – 5,
Nonlinear expansions in reproducing kernel Hilbert spacesOttawa Mathematics and Statistics Conference (OMSC), University of Ottawa, May 24 – 26,
Développements non-linéaires dans des espaces de Hilbert à noyau reproduisant (2nd place at the Three Minute Thesis (3MT) Competition)Ottawa Mathematics and Statistics Conference (OMSC) 2023, University of Ottawa, May 24 – 26,
Développements en série non-linéairesSpectral Geometry and Applications Conference, Université Laval, May 8 – 12
Seminars on Undergraduate Mathematics in Montreal (SUMM), Université de Montréal, Jan. 6 – 8,
Des tours de premiers
2022
Pacific Rim Mathematical Association Congress (PRIMA) (Early Career Research Showcase), Vancouver, Dec. 4 – 9,
Series expansion via unwinding (Poster)CMS Winter Meeting 2022 (AARMS – CMS Student Poster Session), Toronto, Dec. 2 – 5,
Series expansion via unwinding (Winner of the Poster Competition)Québec-Maine Number Theory Conference, Université Laval, Oct. 15 – 16,
Asymptotics for compositions under constraintsA celebration of analytic number theory, a conference in honor of Andrew Granville, Centre de recherches mathématiques (CRM), Sept. 5 – 9
Joint MSRI-BIRS Graduate Summer School - Sums of Squares Method in Geometry, Combinatorics and Optimization, University of British Columbia – Okanagan campus, July 31 – Aug. 13
Ottawa Mathematics Conference (OMC), Online – hosted by the University of Ottawa, July 20 – 23,
Counterexamples to a generalized symmetry conjectureCanadian Undergraduate Mathematics Conference (CUMC), Université Laval, July 13 – 17,
Counterexamples to a generalized symmetry conjectureCMS Summer Meeting 2022 (Harmonic Analysis and PDEs session), St. John's, June 3 – 6,
Unwinding of analytic functions in RKHS and Hardy spacesISM Graduate Student Conference, Université Laval, May 27 – 29,
Contre-exemples à une conjecture de symétrie généraliséeFocus Program on Data Science, Approximation Theory, and Harmonic Analysis, Fields Institute, May 9 – 13
Joint Mathematics Meetings (AMS Special Session on Early Career Number Theory Research with Combinatorics, Modular Forms, and Basic Hypergeometric Series), Online, April 6 – 9
MacMahon Partition Analysis: a discrete approach to broken stick problems
2021
CMS Winter Meeting 2021, Online, Dec. 2-7
Canadian Undergraduate Mathematics Conference (CUMC), Online – hosted by Western University, Aug. 19 – 22,
Plank theorems and their applicationsFUSRP Alumni Research Session, Online – hosted by the Fields Institute, July 23,
Repetitions of multinomial coefficients and a generalization of Singmaster’s conjectureFocus Program on Analytic Function Spaces and their Applications, Online – hosted by the Fields Institute, July 1 – Dec. 31
CMS 75th +1 Anniversary Summer Meeting 2021 (Recent Advances in Complex and Harmonic Analysis session), Online, June 7 – 11
Nonlinear Oscillatory Expansions of Analytic FunctionsISM Graduate Student Conference, Online – hosted by Concordia University, May 22 – 23,
Séries entières aléatoiresSeminars on Undergraduate Mathematics in Montreal (SUMM), Online, Jan. 9 – 10
Une introduction à la théorie des nombres probabiliste
2020
CMS Winter Meeting 2020 (StudC Research Session), Online, Dec. 3 – 8,
MacMahon's Partition Analysis AppliedCMS Winter Meeting 2020 (Recent Advances in Harmonic and Complex Analysis session), Online, Dec. 3 – 8,
Nonlinear Oscillatory Expansions of Holomorphic FunctionsQuébec-Maine Number Theory Conference, Online – hosted by Université Laval, Sept. 26 – 27,
Limiting distributions of sums of random multiplicative functions over function fields (joint with Chenghui Zheng)Canadian Undergraduate Mathematics Conference (CUMC), Online – hosted by Western University, Aug. 20 – 23,
A New Approach to Solve Broken Stick ProblemsYoung Mathematician’s Conference (YMC), Online – hosted by Ohio State University, Aug. 14 – 16,
A New Approach to Solve Broken Stick ProblemsConnecticut Summer School in Number Theory, Online – hosted by the University of Connecticut, June 8 – 12
Seminars on Undergraduate Mathematics in Montreal (SUMM), Université du Québec à Montréal, Jan. 10 – 12,
Une conjecture sur la répétition des coefficients multinomiaux
2019
Maine-Québec Number Theory Conference, University of Maine, Oct. 5 – 6,
Bounds for the counting function of the Jordan-Pólya numbersCanadian Undergraduate Mathematics Conference (CUMC), Queen's University, July 24 – 27,
A Generalization of Singmaster’s Conjecture
William Verreault
Department of Mathematics
University of Toronto, Toronto (ON), M5S 2E4