Yvain Bruned

Yvain Bruned is a Professor of Mathematics at Université de Lorraine, Nancy, France, where he leads research in singular stochastic partial differential equations and related fields. He serves as Principal Investigator for the ERC Starting Grant LoRDeT (2023-2028), which focuses on advancing the theory of decorated trees and Hopf algebraic structures for solving singular SPDEs and dispersive PDEs at low regularity. Previously, he was a Lecturer at the University of Edinburgh (2019-2022) and completed postdoctoral work at Imperial College London and University of Warwick under Martin Hairer.

His educational background includes:

• PhD in Mathematics (2012-2015), UPMC (Paris 6), on "Singular KPZ type equations" under Lorenzo Zambotti
• Master 2 in Probability and Statistics, ENS Cachan / Rennes 1, with honors
• Master 1 in Mathematics, ENS Cachan, with honors
• Bachelor in Mathematics and Computer Science, University of Rennes 1, with honors
• Student at ENS Cachan Brittany extension (2009-2013)
• Classes Préparatoires in Mathematics and Physics (2007-2009)

Bruned's research centers on singular stochastic partial differential equations, with particular focus on Regularity Structures, renormalization theory, and their connections to Hopf algebras. His work bridges theoretical mathematics with applications in quantum field theory, wave turbulence, and numerical analysis. He has developed novel approaches using decorated trees to handle renormalization procedures for singular SPDEs and has extended these methods to dispersive PDEs with random initial data. His research program aims to establish existence and uniqueness results for quasilinear and dispersive SPDEs while developing algebraic tools through deformations of Hopf algebras.

His extensive publication record demonstrates consistent contributions to the field of singular SPDEs, with a clear trajectory from foundational work on Regularity Structures to more recent applications in dispersive PDEs and numerical methods. The publications reveal a strong collaborative network with leading researchers in stochastic analysis, mathematical physics, and algebra. His work shows increasing sophistication in handling renormalization procedures through algebraic structures, with recent papers exploring connections between different mathematical frameworks.

His major scientific recognition includes:

• ERC Starting Grant LoRDeT (2023-2028)

Bruned actively supervises a large group of researchers, currently advising 4 PhD students and 2 postdoctoral researchers at Université de Lorraine, with several former PhD students having completed their degrees at the University of Edinburgh. His ERC grant has enabled him to organize multiple international workshops in Nancy, fostering collaboration between researchers in singular SPDEs, algebraic structures, and numerical analysis. The grant also supports the development of software platforms for decorated trees and their Hopf algebraic structures.

As Principal Investigator of the ERC LoRDeT project, Bruned leads a vibrant research team based at the Elie Cartan Institute of Lorraine, which includes postdocs, PhD students, and visiting researchers. The team regularly organizes specialized workshops on topics including operads, symmetries for quantum field theory, and normal forms for singular dynamics, creating a dynamic research environment that bridges multiple mathematical disciplines.