Website of Pierre-Yves Bienvenu
Who am I?
I am currently a postdoc at the Technische Universität Graz in Austria, in the Institute of Analysis and Number Theory, belonging to the franco-austrian project Arithrand.
Previously, I worked at the Max Planck Institute for Mathematics, Bonn, Germany.
Before that, I was a MiLyon postdoc at
the Institut Camille Jordan (ICJ), Lyon/St-Etienne, France.
I graduated 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."
I also held a Lecturer position at the American University in Paris during Spring 2018.
More details in my CV.
Area of research
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.
Institut für Analysis und Zahlentheorie
I am in office NT 02 028.
e-mail : lastname [at] math.tugraz.at
where lastname is bienvenu.
Publications and preprints
- On algebraic properties of power monoids of numerical monoids (with Alfred Geroldinger). Submitted.
- 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). Submitted.
- 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
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.
- 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.