Welcome to my homepage. I am a differential geometer interested in Lie groupoids, deformation theory, Poisson geometry, and geometry of spaces with singularities, among other things.
Currently I am a researcher at the Centre for Mathematics of the University of Coimbra (CMUC)
Previously I was a graduate student at Utrecht University, a postdoctoral researcher at CMUC, at the Max Planck Institute for Mathematics and at the IME - University of São Paulo, and an associate researcher at the Centre for Mathematics of the University of Porto.
In order to understand the geometry of singular spaces, I study transverse geometry for Lie groupoids. For example, I have been studying transverse measures on Lie groupoids, the role of Lie groupoids in noncommutative geometry, and relations between the theories of proper Lie groupoids and of (particular kinds of) singular Riemannian foliations.
Recently I also started studying formal moduli problems in geometry and algebra.
Preprints
Deformations of symplectic groupoids (with Cristian Cárdenas and Ivan Struchiner)
arXiv:2103.14008 [math.DG]
The transverse density bundle and modular classes of Lie groupoids (with Marius Crainic)
arXiv:2004.06162 [math.DG]
Research papers
Deformations of Lie groupoids (with Marius Crainic and Ivan Struchiner)
Int. Math. Res. Not. IMRN (2020), no. 21, 7662–7746. DOI: 10.1093/imrn/rny221
Suborbifolds and groupoid embeddings (with Martin Weilandt)
North-W. Eur. J. of Math. 6 (2020), 1-18.
Measures on differentiable stacks (with Marius Crainic)
J. Noncommut. Geom 13 (2019), no. 4, 1235-1294. DOI: 10.4171/JNCG/362
Orbispaces as differentiable stratified spaces (with Marius Crainic)
Lett. Math. Phys. 108 (2018), 805–859. DOI: 10.1007/s11005-017-1011-6
Ph.D. Thesis
Differentiable stacks: stratifications, measures and deformations. Utrecht University, 2016.
Advisor: Marius Crainic
Expository papers (in Portuguese)
O princípio do camelo simpléctico
book chapter in "Números, Cirurgias e Nós de Gravata", IST Press, Lisbon 2013;
Co-existência de ciclos num sistema dinâmico
book chapter in "Seminário Diagonal - Proceedings IST, III", Lisbon 2006.
In preparation
Deformations of complex Lie groupoids (with Pier Paolo La Pastina and Luca Vitagliano)
Contact
jnmestre@gmail.com
Sala 5.3
Departamento de Matemática da FCTUC
Largo D. Dinis
3000-143 Coimbra, Portugal