# New CMUP member: Alfonso Tortorella

Nov 08, 2021

On October 1, I joined CMUP as an Assistant Researcher working in the geometry section. For the last three years and an half, I have been an FWO postdoctoral fellow at KU Leuven working with Marco Zambon. Previously, I was a postdoc at CMUC working with Joana Nunes da Costa. In March 2017 I got my PhD at the University of Firenze under the supervision of Paolo de Bartolomeis and Luca Vitagliano. In 2015, as a WCMCS PhD intern, I worked at IMPAN (Warsaw) with Janusz Grabowski.

I work in the area of Poisson geometry, meant in the broad sense of the term. My main research interests are deformation theory, normal form theorems and Jacobi geometry. The techniques required in my research activity include Lie groupoids and algebroids, geometry of PDEs, graded geometry and $L_\infty$ algebras. My PhD focused on deformations of coisotropic submanifolds in symplectic/Poisson and contact/Jacobi manifolds. This problem was originally motivated by Kapustin and Orlov's work on branes, Mirror Symmetry and Fukaya category.

My main result was the construction of the $L_\infty$ algebra controlling the deformation problem in the Jacobi setting. I also exhibited, in the contact setting, a class of coisotropic submanifolds rigid under deformations, and the first example of an obstructed coisotropic submanifold. Further, we defined homotopy Jacobi structures analysing their main properties.

Since then I have continued working on deformation problems in Poisson and related geometries developing, in particular, the deformation theories for symplectic foliations and Dirac--Jacobi structures.

As additional research directions, motivated by contact groupoids, I got interested in multiplicative structures and developed the Lie theory of multiplicative derivations of VB-groupoids. Recently, studying the local structure of Jacobi manifolds, we introduced and investigated contact dual pairs as the first step towards Morita equivalence and Picard groups of contact groupoids. Further, we introduced homogeneous G-structures as a conceptually well-grounded solution to the anomaly that, unlike symplectic structures, contact structures do not fit in the framework of G-structures.