Broadly speaking, my research interests lie in the field of differential geometry and its interplay with mathematical physics.

I work with higher geometry methods in multisymplectic geometry and, most of all, I am interested in structures “up to homotopies” inspired by geometry and mechanics.

My research project focuses on the notions of L_{∞} algebra of observables and homotopy comomentum maps. These are the higher analogues of smooth observables and the ordinary comoment map in the context of n-plectic geometry.
My key results are related to the explicit construction of non-trivial instances of these objects with possible application in different areas of mathematics (e.g. knot theory) and physics (e.g. hydrodynamics).

Nowadays, I am investigating the notion of gauge transformations and (symplectic) reduction in the context of multisymplectic geometry.

A deep motivation for pursuing this line of research can be tracked in my interest in understanding the axiomatic and geometric foundation of classical field theories (i.e. mechanical systems with infinite and continuous degrees of freedom). In this perspective, I am always interested in expanding my knowledge both in the pure direction (homotopical algebra, higher categories) than in the applied direction (symplectic integrators, numerical simulations).

- Multi-symplectic geometry and L
_{∞}-Algebras - Higher structures and Homotopy structures
- Axiomatization and mathematical foundations of classical and quantum field theories
- Geometric Mechanics of Field Systems
- Geometric and Algebraic Quantization

Sep 2022 | Observables of multisymplectic manifolds and higher Courant algebroids.Miti A. M. and Zambon M. ; arXiv:2209.05836. [bibtex] [arxiv] |

Jun 2022 | Reduction of L∞-algebras of observables on multisymplectic manifolds.Blacker C. , Miti A. M. and Ryvkin L. ; arXiv:2206.03137. [bibtex] [arxiv] |

Feb 2021 | A Hydrodynamical Homotopy Co-momentum Map And A Multisymplectic Interpretation Of Higher-order Linking Numbers.Miti A. M. and Spera M. ; Journal of the Australian Mathematical Society. [bibtex] [arxiv] |

Dec 2020 | Multisymplectic actions of compact Lie groups on spheres.Miti A. M. and Ryvkin L. ; Journal of Symplectic Geometry. [bibtex] [arxiv] |

Aug 2020 | Derivation of the HOMFLYPT knot polynomial via helicity and geometric quantization.Miti A. M. and Spera M. ; Bollettino dell'Unione Matematica Italiana. [bibtex] [arxiv] |

Apr 2021 | Homotopy comomentum maps in multisymplectic geometry.Phd thesis @ Università Cattolica del Sacro Cuore & KU Leuven; Advisors: Mauro Spera, Marco Zambon. [bibtex] [file] |

Nov 2015 | Algebraic quantization of Jacobi fields and geometrica approach to Peierels brackets.Master Thesis @ Università Degli Studi di Milano; Advisors: Claudio Dappiaggi, Livio Pizzocchero. [bibtex] [file] |

Nov 2010 | Teoria dei gruppi di Lie e applicazione alla meccanica del corpo rigido.Bachelor thesis @ Università degli Studi di Milano Bicocca; Advisors: Franco Magri. [bibtex] [file] |

May 2024 | Multisymplectic approach to LFT and the Stress-Energy tensor.Talk @ Geometric conservation laws in physics, Università di Torino. [Slides] |

Mar 2024 | Multisymplectic observables and higher Courant algebroids.Talk @ Higher structures in Caprarola, INFN, Caprarola. [Slides] |

Jul 2023 | The multisymplectic structure of Lagrangian field theories.Talk @ Higher structures working group, UniGoettingen, Gottingen. [Slides] |

May 2023 | Symmetries and reduction of multisymplectic manifolds.Talk @ Joint seminar in mathematical physics, UniPv, Pavia. [Slides] |

Feb 2023 | On the Lie infinity algebra associated to higher Courant algebroids.Talk @ Higher structures working group, ICJ, Lyon. [Slides] |

Jan 2023 | First steps in geometric quantum mechanics.Talk @ PhD Seminar, UCSC, Brescia. [Slides] |

Dec 2022 | Multisymplectic observables and higher Courant algebroids.Talk @ Séminaire Physique mathématique, ICJ, Lyon. [Slides] |

Aug 2022 | Symmetries and reduction of multisymplectic manifolds.Talk @ Higher Structures and Field Theory, Esi, Vienna. [Slides] |

Jun 2022 | L∞-structures via the Nijenhuis-Richardson algebra.Talk @ Good Morning Sfars, online. [Slides] |

Apr 2022 | Symmetries and reduction of multisymplectic manifolds.Talk @ MPI-Oberseminar, MPIM, Bonn. [Slides] |

Mar 2022 | Morphisms and Yoneda lemma for stacks.Talk @ Reading seminars on differentiable stacks, MPIM, Bonn. [Slides] |

Dec 2021 | Gauge transformations of multisymplectic manifolds and L-infinity observables.Talk @ Higher geometry seminar, MPIM, Bonn. [Slides] |

Jul 2021 | Gauge transformations of multisymplectic manifolds and L-infinity observables.Talk @ Young Researchers' Virtual Multisymplectic Geometry Conference, EIMI, Saint Petersburg. [Slides] |

Apr 2021 | What is: Geometric mechanics?.Talk @ PhD colloquium, KU Leuven. [Slides] |

Feb 2021 | Phd Preliminary Defence.Talk @ -, KU Leuven. [Slides] |

Sep 2020 | Homotopy co-moment maps for compact actions on spheres.Talk @ Workshop on Multisymplectic Geometry, KU Leuven. [Slides] |

May 2020 | Gauge transformations of multisymplectic manifolds and L_infinity observables.Talk @ Poisson seminar, KU Leuven. [Slides] |

Dec 2019 | MultiSymplectic manifolds and homotopy co-momentum maps.Poster @ Supergeometry conference, Luxembourg. [Slides] |

Mar 2019 | Multisymplectic Geometry and Knots.Talk @ UniSa, Fisciano. [Slides] |

Dec 2018 | Homotopy co-momentum Map in Hydrodynamics.Talk @ 13th GMC Young researcher's workshop, Coimbra. [Slides] |

May 2018 | On some (multi)symplectic aspects of link invariants.Talk @ -, KU Leuven. [Slides] |

Nov 2017 | An invitation to Geometric Mechanics.Talk @ UCSC, Brescia. [Slides] |

Jul 2017 | Multi-symplectic Geometry and Covariant Phase Space.Poster @ 11th GMC summer school, ICMAT, Madrid. [Slides] |

Feb 2019 | MultiSymplectic Geometry and Classical Field systems. (WIP)On the multisymplectic framework of classical field theories. [Notes] |

Feb 2018 | Duffing system in Python.Solving Duffing Equation by means of Runge-Kutta method. [Code] |

Oct 2017 | Cartan calculus on smooth manifolds.A compact cheatsheet with the basic computation rules. [Notes] |

May 2017 | Covariant Phase Space Via Multysimplectic Geometry.On the covariant phase space in the multisymplectic framework. [Notes] |