Publications

Research papers (peer reviewed)

1. MC, On deformations of multidimensional Poisson brackets of hydrodynamic type.
   Commun. Math. Phys. vol. 335(2) 2015, 851-894,  https://doi.org/10.1007/s00220-014-2219-2

2. MC, Dispersive deformations of the Hamiltonian structure of Euler's equations.
   Theoretical and Mathematical Physics (2016) 188:1296,  https://doi.org/10.1134/S0040577916090026

3. G. Carlet, MC, S. Shadrin, Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets.
   J. Geom Phys. (2017) 114:404,  https://doi.org/10.1016/j.geomphys.2016.12.008.

4. MC, D. Valeri, MasterPVA and WAlg: Mathematica packages for Poisson Vertex Algebras and classical affine W-algebras.
   Boll. Unione Mat. Ital. (2018) 11: 503, https://doi.org/10.1007/s40574-017-0146-9.

5. MC, Higher order dispersive deformations of multidimensional Poisson brackets of hydrodynamic type.
   Theoretical and Mathematical Physics (2018) 196 (2). pp. 1129-1149, https://doi.org/10.1134/S0040577918080032

6. G. Carlet, MC, S. Shadrin, Normal form of dispersive scalar Poisson brackets with two independent variables.
   Lett. Math. Phys. (2018) 108:2229. https://doi.org/10.1007/s11005-018-1076-x

7. MC, E. V. Ferapontov, M. Pavlov, R. Vitolo, On a class of third-order nonlocal Hamiltonian operators.
   J. Geom. Phys. (2018) 138:285, https://doi.org/10.1016/j.geomphys.2018.10.018

8. MC, J. P. Wang, A Darboux-Getzler theorem for scalar difference Hamiltonian operators.
   Commun. Math. Phys. (2020) 374:1497 https://10.1007/s00220-019-03497-2

9. MC, P. Lorenzoni, R. Vitolo, Three computational approaches to weakly nonlocal Poisson brackets.
   Stud. Appl. Math.(2020) 144:412–448, https://doi.org/10.1111/sapm.12302

10. MC, J. P. Wang, Recursion and Hamiltonian operators for integrable nonabelian difference equations.
    Nonlinearity (2021) 34:205 https://doi.org/10.1088/1361-6544/aba88c/

11. MC, P. Lorenzoni, D. Valeri, R. Vitolo, Weakly nonlocal Poisson brackets: tools, examples, computations.
    Comput. Phys. Commun. (2022) 274:108284 https://doi.org/10.1016/j.cpc.2022.108284

12. MC, J. P. Wang. Hamiltonian structures for integrable nonabelian difference equations.
    Commun. Math. Phys. (2022) 392, 219-278 https://doi.org/10.1007/s00220-022-04348-3

13. MC, D. Zhang. Multidimensional integrable deformations of integrable PDEs.
    J. Phys. A: Math. Theor. (2023) 56:505701 https://doi.org/10.1088/1751-8121/ad0ac8

Preprints (full list)

Access all my preprints on arXiv

Education & Outreach

Since my years as a PhD student I have been involved in outreach activities for school students and the general public; I have written (and recorded some videos) for middle-school textbooks in Mathematics (the material is copyrighted: if I am not mistaken one might be able to find it in Flaccavento Romano, Obiettivo Competenze, Fabbri Editori), as well as held public seminars, hands-on laboratories and participated with a few talks to the outreach program SISSA for schools.

In 2018 I gave a seminar in history of geometry about Star Polygons (actually twice: once for graduate students and once for secondary school students). The slides for the grad students version can be found here

In December 2019 I gave a (simple) talk at the meeting Orlando Reloaded - Alla ricerca del metodo nel diritto pubblico (a public law conference) about  mathematical methods and proving theorems. The preprint of my contribution to be published in the proceedings may be found here. There is also a public recording of my lecture on youtube (everything in Italian)