Research

My field of research includes singular foliations, Lie algebroids, and their ’higher’ counterparts such as Lie ∞-structures on graded manifolds. My interest lies in the understanding of singularities and singular foliation invariants with the help of higher structures. This algebraic approach is justified by the fact that singularities in foliation theory carry information that may not be caught by a pure geometric analysis. I am also interested in related problems involving Lie ∞-algebroids, such as homotopy categories, holonomy groupoids, gauging procedures in supergravity, and the BFV-BRST formalism in gauge theories.

Recently, after an additional curriculum in sociology and in philosophy of science, I got caught in the philosophy of mathematical practice. In contrast with the foundationalist and the logicist traditions that have been prevalent in the philosophy of mathematics during the XXth century, this intellectual movement advocates the study of praxis in philosophical inquiry. On this side of my research work, I am currently striving to develop stronger ties between the sociology of science and the philosophy of mathematical practice.

 

Publications
Maths and Physics

S. L. and J. Stasheff, From differential crossed modules to tensor hierarchies. arXiv:2003.07838

S. L. and J. Palmkvist, Infinity-enhancing of Leibniz algebras, Lett. Math. Phys. (2020) 110(11):3121-3152. arXiv:1907.05752

C. Laurent-Gengoux, S. L. and T. Strobl, The universal Lie ∞-algebroid of a singular foliation. Doc. Math. (2020) 25:1571-1652. arXiv:1806.00475

S. L., Tensor hierarchies and Leibniz algebras, J. Geom. Phys. (2019) 144:147-189. arXiv:1708.07068

S. L., A short guide through integration theorems of generalized distributions, Differ. Geom. Appl. (2018) 61:42-58. arXiv:1710.01627

S. L., H. Samtleben and T. Strobl, Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions, J. Geom. Phys. (2014) 86:497-533. arXiv:1403.7114

Philosophy and Sociology of science

S. L., Qu’est-ce qu’un théorème (en pratique) ?, Rev. Anthropol. Connaiss. (2021) 15(2). open-edition:rac/22479

J. Larregue, S. L. and M. Khelfaoui, La sociobiologie est morte, vive la psychologie évolutionniste ! Zilsel (2021) 8:104-143. HAL-SHS:03201759

 
Sylvain Lavau | Research