(version française)

I am currently a Teaching Fellow at the Trinity College Dublin, in the School of Mathematics. Previous appointments

- 2021-2022: postdoc at the Technische Universität Graz in Austria, in the Institute of Analysis and Number Theory, belonging to the franco-austrian project Arithrand.
- 2020-2021: postdoc at the Max Planck Institute for Mathematics, Bonn, Germany.
- 2018-2020: MiLyon postdoc at the Institut Camille Jordan (ICJ), Lyon/St-Etienne, France.
- Spring 2018: Lecturer at the American University in Paris.
- 2014-2018: PhD at the University of Bristol, where my PhD supervisor was Julia Wolf. My doctoral thesis, which I defended in June 2018, was entitled "Linear, bilinear and polynomial configurations in function fields and the primes."

More details in my CV.

My research combines analytic, combinatorial, probabilistic and algebraic methods to solve arithmetical problems. It belongs to the area called arithmetic combinatorics, which has intense interactions with number theory, extremal combinatorics, harmonic analysis, ergodic theory, and various topics of theoretical computer science, such as error correcting codes, pseudorandomness etc.

A few keywords:

- Higher order Fourier analysis.
- Configurations of prime numbers, Green-Tao method.
- Finite fields and polynomial rings over them.
- Sum-product estimates.
- Density of sumsets.

Trinity College Dublin

College Green

Dublin 2

Ireland

My office there is 20.31 (House 20, Westland Row).

__ e-mail__ : bienvenp [at] tcd.ie

- On algebraic properties of power monoids of numerical monoids (with Alfred Geroldinger). Accepted in
*Isr. J. Math*. - Metric decomposability theorems on sets of integers. Submitted.
- A transference principle for systems of linear equations, and applications to almost twin primes (with Fernando Shao and Joni Teräväinen). Accepted in
*Algebra and Number Theory.* - On additive bases in infinite abelian semigroups (with Benjamin Girard and Thai Hoang Lê). Accepted in
*J. Comb. Algebra*. - Kneser's theorem in sigma-finite Abelian groups (with François Hennecart). Accepted for publication in the
*Canadian Mathematical Bulletin*. - On the density or measure of sets and their sumsets in the integers or the circle (with François Hennecart).

*Journal of Number Theory***212**(2020), 285–310. - A note on the Bilinear Bogolyubov Theorem: Transverse and bilinear sets (with Angel Martinez and
Diego Gonzalez).

*Proceedings of the American Mathematical Society***148**(2020), 23-31. - A note on the set A(A+A) (with François Hennecart et Ilya Shkredov).

*Moscow Journal of Combinatorics and Number theory***8**(2019), no. 2, 179-188. - Linear and quadratic uniformity of the Möbius function over F_q[t] (with Thai Hoang Lê).

*Mathematika***65**(2019), no. 3, 505–529. - A bilinear Bogolyubov theorem (with Thai Hoang Lê).

*European Journal of Combinatorics***77**(2019), 102–113. - Polynomial equations in function fields.

*Oxford Quarterly Journal of Mathematics***68**(2017), no. 4, 1395–1398. - A Higher-Dimensional Siegel-Walfisz theorem.

*Acta Arithmetica***179**(2017), no. 1, 79–100. - Asymptotics for some polynomial patterns in the primes.

*Proceedings of the Royal Society of Edinburgh Section A***149**(2019), no. 5, 1241–1290.

I also write a mathematical blog.

- Michaelmas term 2022:
- Hillary Term 2023:

- Spring 2022: I taught a master's level course of Combinatorial and Additive Number Theory at TU Graz.
- Spring 2020: exercise classes of Probability theory in Jussieu (second year)
- Automn 2019: exercise sessions of graph theory and optimisation at Télécom Saint-Étienne.
- Spring 2018: lecturer at the
American University in Paris.
I taught
*Precalculus*and*Applied Statistics*. - 2014-2016: in Bristol, I was teaching assistant in various courses.