Research interests

• Variational analysis of atomistic and continuous physical systems
• Analysis of problems with multiple scales
• Nonlinear-nonlocal problems in Continuum Mechanics
• Stability of Geometric and functional inequalities

Short CV

• 2012 - Professor at TU München
• 2005 - 2012 Assistant Professor at University of Naples
• 2004 - 2005 Research contract at SISSA (Functional Analysis Group with Prof. G. Dal Maso)
• 2004 PhD University of Naples (advisor: Prof. A. Braides)

Editorial Activity

• Associate Editor for Acta Applicandae Mathematicae
• Associate Editor for Mathematics in Engineering

Books

Discrete Variational Problems with Interfaces (with R. Alicandro, A.Braides and M. Solci) Cambridge University Press 2023 (doi: 10.1017/9781009298766)

Publications

1. The quantitative Faber-Krahn inequality for the combinatorial Laplacian in Z^d (with L. Kreutz, G.P. Leonardi and G. Morselli), 2025 [preprint]
2. Energy concentration in a two-dimensional magnetic skyrmion model: variational analysis of lattice and continuum theories (with L. Kreutz and L. Briani), (2025) [preprint]
3. Consistency for the surface diffusion flat flow in three dimensions (with N. Fusco, V. Julin and A. Kubin), (2025) [preprint]
4. From discrete to continuum in the helical XY-model: emergence of chirality transitions in the S^1 to S^2 limit (with D. Reggiani and F. Solombrino), (2024) [preprint]
5. A notion of s-fractional mass for 1-currents in higher codimension (with T. Heilmann, A. Kubin, F. Onoue and M. Ponsiglione) (2024) [Preprint]
6. Surfactants in a non-local model for phase transitions (with T. Heilmann), ESAIM: Cocv, to appear (2024) [Preprint]
7. Stacking faults in the limit of a discrete model for partial edge dislocations (with A. Bach, A. Garroni and G. Orlando), Arch. Rat. Mech. Anal., to appear,  (2024) [Preprint]
8. Surfactants in the Two Gradient Theory of Phase Transitions (with T. Heilmann) (2024) [preprint]
9. Discrete and Continuum Area-Preserving Mean-Curvature Flow of Rectangles (with A. Kubin), Ann. Scuola Norm. Sup. Pisa Cl. Sci., to appear (2024)  [preprint]
10. Screw dislocations in periodic media: variational coarse graining of the discrete elastic energy (with R. Alicandro and L. De Luca), Nonlinear Analysis., 231 (2023) Paper No. 112871, 21 pp. [preprint]
11. Emergence of Wulff-Crystals from atomistic systems on the FCC and HCP lattices (with L. Kreutz and G.P. Leonardi), Commun. Math. Phys., 402 (3), 2931-2978, (2023) [preprint]
12. Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds (with R. Badal),  Calc. Var. PDEs, to appear, (2022) [preprint]
13. A classical S^2 spin system with discrete out-of-plane anisotropy: variational analysis at surface and vortex scalings (with G. Orlando and M. Ruf), Nonlinear Analysis., 231 (2023), Paper No. 112929, 33 pp [preprint]
14. Screw dislocations in periodic media: variational coarse graining of the discrete elastic energy (with R. Alicandro and L. De Luca), Nonlinear Analysis., 231  (2023), Paper No. 112871, 21 pp. [preprint]
15. Variational analysis of the J_1-J_2-J_3 model: a nonlinear lattice version of the Aviles-Giga functional (with M. Forster and G. Orlando), Arch. Rat. Mech. Anal., 245 (2022), no. 2, 1059–1133. [preprint]
16. Phase-field approximation of functionals defined on piecewise-rigid maps (with M. Focardi and C.I. Zeppieri), Journal of Nonlinear Science, (2021) 31:78 [preprint]
17. Topological singularities in periodic media: Ginzburg-Landau and core-radius approaches (with R. Alicandro, A. Braides, L. De Luca and A. Piatnitski), Arch. Rat. Mech. Anal., 243 no. 2 (2022), 559-609 [preprint]
18. The N-clock model: variational analysis for fast and slow divergence rates of N (with G. Orlando and M. Ruf), Arch. Rat. Mech. Anal., 245 (2022), no. 2, 1135–1196. [preprint]
19. The antiferromagnetic XY model on the triangular lattice: Topological singularities (with A. Bach, L. Kreutz and G. Orlando), Indiana Univ. Mat. J., 71 (2022), no.6, 2411–2475. [preprint]
20. The antiferromagnetic XY model on the triangular lattice: Chirality transitions at the surface scaling (with A. Bach, L. Kreutz and G. Orlando), Calc. Var. PDEs (2021) 60:149 [preprint]
21. Coarse graining and large-N behaviour of the d-dimensional N-clock model (with G. Orlando and M. Ruf), Interfaces and Free Boundaries , 23 no. 3 (2021), 323-351 [preprint]
22. From the N-clock model to the XY model: emergence of concentration effects in the variational analysis (with G. Orlando and M. Ruf), Comm. Pure Appl. Math., 75 (2022), no. 10, 2279-2342. [preprint]
23. Discrete-to-continuum limits of multi-body systems with bulk and surface long-range interactions (with A. Bach and A. Braides) SIAM J. Math. Anal., 52 (2020) no. 4, 3600-3665 [preprint]
24. Variational analysis of a two-dimensional frustrated spin system: emergence and rigidity of chirality transitions (with M. Forster and G. Orlando), SIAM J. Math. Anal., 51 no.2 (2019), 4848-4893 [preprint]
25. Random finite-difference discretizations of the Ambrosio-Tortorelli functional with optimal mesh size (with A. Bach and M. Ruf), SIAM J. Math. Anal., 53 no. 2 (2021), 2275-2318 [preprint]
26. Maximal fluctuations on periodic lattices: an approach via quantitative Wulff inequalities (with G.P. Leonardi), Commun. Math. Phys., 375, (2020), 1931–1944 [preprint]
27. From statistical polymer physics to nonlinear elasticity (with A. Gloria and M. Ruf), Arch. Rat. Mech. Anal., 236, (2020), 1127-1215 [preprint]
28. A note on relaxation with constraints on the determinant (with N. Fusco), ESAIM: Cocv, (2019), vol. 25, no.41, 1-15 [preprint]
29. Hemihelical local minimizers in prestrained elastic bi-strips (with M. Ruf and F. Solombrino), Zeitschrift für angewandte Mathematik und Physik, (2017), 68:122 [preprint]
30. Gamma-convergence analysis of a generalized XY model: fractional vortices and string defects (with R. Badal, L. De Luca and M. Ponsiglione), Commun. Math. Phys. 358, (2018), no. 2, 705–739. [preprint]
31. Continuum limit and stochastic homogenization of discrete ferromagnetic thin films (with M. Ruf and A. Braides), Analysis & PDE, (2018), vol. 11, no.2, 499-553 [preprint]
32. On global and local minimizers of prestrained thin elastic rods (with M. Ruf and F. Solombrino), Calc. Var. PDEs, (2017), 56:115 [preprint]
33. Crystalline Motion of Interfaces Between Patterns (with A. Braides and N.K. Yip), J. Stat. Phys., 165, (2016), no. 2, 74-319 [preprint]
34. Ground states of a two-phase model with cross and self attractive interactions (with L. De Luca, M. Novaga and M. Ponsiglione), SIAM J. Math. Anal., 48 (2016), no. 5, 3412–3443 [preprint]
35. Interfaces, modulated phases and textures in lattice systems (with A. Braides), Arch. Rat. Mech. Anal., 223, (2017), 977-1017 [preprint]
36. Discrete spin systems on random lattices at the bulk scaling (with M. Ruf), Disc. Cont. Dyn. Sys.-S, 10, (2017), no.1, 101-117 [preprint]
37. Chirality transitions in frustrated S2-valued spin systems (with F. Solombrino and M. Ruf), Math. Models Methods Appl. Sci., 26, (2016), no. 8, 1481-1529 [preprint]
38. Improved convergence theorems for bubble clusters. I. The planar case (with G.P. Leonardi and F. Maggi), Indiana Univ. Mat. J., 65, (2016), 1979-2050 [preprint]
39. Domain formation in magnetic polymer composites: an approach via stochastic homogenization (with R. Alicandro and M. Ruf), Arch. Rat. Mech. Anal., 218, (2015), no. 2, 945-984 [preprint]
40. Frustrated ferromagnetic spin chains: a variational approach to chirality transitions (with F. Solombrino), Journal of Nonlinear Science, 25, (2015), no.2, 291-313 [preprint]
41. Q-tensor continuum energies as limits of head-to-tail symmetric spin systems (with A. Braides and F. Solombrino), SIAM J. Math. Anal., 47, (2015), 2832–2867, [preprint]
42. Sharp stability inequalities for planar double bubbles (with G.P. Leonardi and F. Maggi), Interfaces and free boundaries, 19(3) (2017), 305–350 [preprint]
43. Droplet Minimizers of an Isoperimetric Problem with long-range interactions (with E.N. Spadaro), Communications on Pure and Applied Mathematics, 66, (2013), no.28, 1298-1333 [preprint]
44. Best constants for the isoperimetric inequality in quantitative form (with G.P. Leonardi), J. Eur. Math. Soc., 15, (2013), no.3, 1101-1129, [preprint]
45. A selection principle for the sharp quantitative isoperimetric inequality (with G.P. Leonardi), Arch. Rat. Mech. Anal., 206, (2012), no.2, 617-643 [preprint]
46. Phase transitions in presence of surfactant: from discrete to continuum (with R. Alicandro and L. Sigalotti), Interfaces and free boundaries, 14, (2012), no.1, 65-103 [preprint]
47. Asymptotic analysis of a second-order singular perturbation model for phase transitions (with E.N. Spadaro and C.I. Zeppieri ), Calc. Var. and PDE, 41, (2011), no.1-2, 127-150 [preprint]
48. Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity (with R. Alicandro and A. Gloria), Arch. Rat. Mech. Anal., 200, (2011), no. 3, 881-942 [preprint]
49. Variational equivalence between Ginzburg-Landau, XY spin systems and screw dislocation energies (with R. Alicandro and M. Ponsiglione), Indiana Univ. Math. J., 60, (2011), no.1, 171-208 [preprint]
50. The Gibbs-Thomson relation for non homogeneous anisotropic phase transitions (with Y. Nagase and G. Pisante), Advances in Calculus of Variations, 3, (2010), no. 3, 321-344 [preprint]
51. Discrete-to-continuum limits for strain-alignment-coupled systems: magnetostrictive solids, ferroelectric crystals and nematic elastomers (with A. De Simone and C.I. Zeppieri), Networks and Heterogeneous Media 4, (2009), no. 4, 667-708 [preprint]
52. Variational analysis of the asymptotics of the XY model (with R. Alicandro), Arch. Rat. Mech. Anal. 192, (2009), no. 3, 501-536 [preprint]
53. A variational description of bulk energies for bounded and unbounded spin systems (with R. Alicandro and A. Gloria), Nonlinearity 21, (2008), no. 8, 1881-1910 [preprint]
54. Continuum limits of discrete thin films with superlinear growth densities (with R. Alicandro and A. Braides), Calc. Var. and PDE 33, (2008), no. 3, 267-297 [preprint]
55. Mathematical derivation of a rubber-like stored energy functional (with R. Alicandro and A. Gloria), C. R. Acad. Sci. Paris, Ser. I 345, (2007), 479-482 [preprint]
56. A sharp estimate of the extinction time for the mean curvature flow (with B.Brandolini, C. Nitsch and C. Trombetti), Appl. Math. Lett. 20, (2007), no. 5, 551-557
57. Surface energies in nonconvex discrete systems (with A. Braides) Math. Models Methods Appl. Sci.,17, (2007), no. 7, 985-1037 [preprint]
58. Phase and antiphase boundaries in binary discrete systems: a variational viewpoint (with R. Alicandro and A. Braides), Networks and Heterogeneous Media, 1, (2006), no. 1, 85-107 [preprint]
59. Some remarks on the extinction time for the mean curvature flow (with B.Brandolini, C. Nitsch and C. Trombetti), Le Matematiche , 60, (2005), 411-417
60. L^∞ energies on discontinuous functions (with R. Alicandro and A. Braides), Discrete and Continuous Dynamical Systems, 12, (2005), 905-928 [preprint]
61. A general integral representation result for continuum limits of discrete energies with superlinear growth, (with R. Alicandro) SIAM J. Math. Anal. 36, (2004), 1-37 [preprint]
62. Asymptotic behaviour of solutions to p-laplacian equation, (with C. Trombetti), Asymptotic Analysis 35, (2003), 27-40

Other Publications

1. A maximal fluctuation estimate of Wulff shapes on 2d lattices, Oberwolfach Rep. (2018)
2. Atomistic-to-continuum variational analysis of random lattice systems, Oberwolfach Rep., 35, (2015)
3. Chirality transitions in frustrated ferromagnetic chains, PAMM Proc. Appl. Math. Mech. 15, (2015), 23 – 26
4. Interfaces of discrete patterns, Oberwolfach Rep., 10 (2013)
5. The XY spin system and the Ginzburg-Landau energy, Oberwolfach Rep., 5 no. 2 (2008), 1126-1129
6. Convergence analysis of the Böl-Reese discrete model for rubber (with R. Alicandro and A. Gloria), in Continuum Models and Discrete Systems; Cmds 11 (D. Jeulin and S. Forest eds), Presses De L'Ecole Des Mines, 2008
7. Dimension reduction for discrete systems (with R. Alicandro and A. Braides), in Applied and Industrial Mathematics in Italy II (G.Fotia, L.Puccio eds.), World Sci. (2007), 25-36
8. Boundary layer energies in discrete systems: an approach via Gamma-convergence, in Communication to SIMAI Congress,Vol. 1 (2006)
9. Dimension reduction for discrete systems, in Communication to SIMAI Congress,Vol. 1 (2006)
10. Surface energies in discrete systems, Oberwolfach Reports, 1 (2004), no. 3, 1564-1565
11. Multiscale analysis for nonlinear variational problems arising from discrete system, Ph.D. Thesis (2004)