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.


Email william.verreault@utoronto.ca

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


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2020 


2019  

William Verreault

Department of Mathematics

University of Toronto, Toronto (ON), M5S 2E4

william.verreault@utoronto.ca