- Calculus of variations and partial differential equations
- Homogenisation (deterministic and stochastic)
- Harmonic analysis

I am interested in several applications in material science:

- plasticity and dislocations
- non-local aggregation problems
- nonlinear elasticity and rod and plate theories
- fracture and damage theories

- L. Scardia: The nonlinear bending-torsion theory for curved rods as Gamma-limit of three-dimensional elasticity.
*Asymptot. Anal.*, 47 (2006) 317-343. - L. Scardia: Damage as Gamma-limit of microfractures in anti-plane linearized elasticity.
*Math. Models Methods Appl. Sci.*, 18 (2008) 1703-1740. - L. Scardia: Asymptotic models for curved rods derived from nonlinear elasticity by Gamma-convergence.
*Proc. Roy. Edinb. Soc. A*, 139 (2009), 1037-1070. - T. Roubicek, L. Scardia and C. Zanini: Quasistatic delamination problem.
*Contin. Mech. Thermodyn.*, 21 (2009), 223-235. - L. Scardia: Damage as the Gamma-limit of microfractures in linearized elasticity under the non-interpenetration constraint.
*Adv. Calc. Var.*, 3 (2010), 423-458. - F. Cagnetti and L. Scardia: An extension theorem in
*SBV*and an application to the homogenization of the Mumford-Shah functional in perforated domains.*J. Math. Pures Appl.*, 95 (2011), 349-381. - L. Scardia, A. Schloemerkemper and C. Zanini: Boundary layer energies for nonconvex discrete energies.
*Math. Models Methods Appl. Sci.*, 21 (2011), 777-817. - M.G. Mora and L. Scardia: Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density.
*J. Differential Equations*, 252 (2012), 35-55. - L. Scardia, A. Schloemerkemper and C. Zanini: Towards uniformly Gamma-equivalent theories for non-convex discrete systems.
*Discrete Contin. Dyn. Syst. Ser. B*, 17/2 (2012), 661-686. - L. Scardia and C.I. Zeppieri: Line Tension for Plasticity as the Gamma-limit of a nonlinear dislocation energy.
*SIAM J. Math. Anal.*, 44/4 (2012), 2372-2400. - M.G.D. Geers, R.H.J. Peerlings, M.A. Peletier and L. Scardia: Asymptotic behaviour of a pile-up of infinite walls of edge dislocations.
*Arch. Rational Mech. Anal.*, 209/2 (2013), 495-539. - L. Scardia, R.H.J. Peerlings, M.A. Peletier and M.G.D. Geers: Mechanics of dislocation pile-up: A unification of scaling regimes.
*J. Mech. Phys. Solids*, 70 (2014), 42-61. - S. Mueller, L. Scardia and C.I. Zeppieri: Geometric rigidity for incompatible fields and an application to stain-gradient plasticity.
*Indiana Univ. Math. J.*, 63 (2014), 1365-1396. - S. Mueller, L. Scardia and C.I. Zeppieri: Gradient theory for geometrically nonlinear plasticity via the homogenization of dislocations. In: Conti, S. and Hackl, K., eds. Analysis and Computation of Microstructure in Finite Plasticity. Switzerland: Springer (2015), 175-204.
- A. Garroni, P. van Meurs, M.A. Peletier and L. Scardia: Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock.
*Math. Models Methods Appl. Sci.*, 21 (2016). - L. Scardia: Continuum limits of discrete models via Gamma-convergence. In: Muntean et al eds. Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity. Lect. Notes Appl. Math. Mech., 3, Springer (2016), 145-186.
- M.G. Mora, M.A. Peletier and L. Scardia: Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement.
*SIAM J. Math. Anal.*, in press. - M.G. Mora, L. Rondi and L. Scardia: The equilibrium measure for a nonlocal dislocation energy.
*Comm. Pure Appl. Math.*, in press. - J.A. Carrillo, J. Mateu, M.G. Mora, L. Rondi L. Scardia and J. Verdera: The ellipse law: Kirchhoff meets dislocations. Submitted.
- F. Cagnetti, G. Dal Maso, L. Scardia and C.I. Zeppieri: Gamma-convergence of free discontinuity problems. Submitted.
- F. Cagnetti, G. Dal Maso, L. Scardia and C.I. Zeppieri: Stochastic Homogenisation of Free-Discontinuity Problems. Submitted.

- 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taiwan, 5-9 July 2018.
- Topics in the Calculus of Variations: Recent Advances and New Trends, Banff, 20-25 May 2018.
- Operators and Spectral theory, University of Reading, 4 April 2018.
- University of Edinburgh, 26 February 2018.
- University of Cardiff, 12 February 2018.
- Variational Methods for the Modelling of Inelastic Solids, Oberwolfach, 4-10 February 2018.
- Mini workshop on Analysis and Probability, University of Sussex, 22-25 January 2018.
- Variational Approaches to Problems in Solid Mechanics , University of Warwick, 18 December 2017.
- University of Pavia, 23-29 October 2017.
- Material Theories, Oberwolfach, 16-22 July 2017.
- Workshop on "Aggregation-Diffusion PDEs:Variational Principles, Nonlocality and Systems", Anacapri, Italy, 10-14 July, 2017.
- BIRS Workshop "Analysis of Dislocation Models for Crystal Defects", Oaxaca (CMO, Mexico), 25-30 June 2017.
- Institut Henri Poincare, Paris, 15-16 June 2017.
- 7th meeting of the Reading-Bath-Cardiff network on generalised solutions for nonlinear PDE, University of Reading, 14 June 2017.
- Non-local equations and fractional diffusion, University of Warwick, 22-26 May 2017.
- Miniworkshop on dislocations, plasticity, and fracture, SISSA, Trieste, Italy, 13-16 February 2017.
- University of Warwick, 3 February 2017.
- University of Oxford, 7 November 2016.
- Shanghai Jiao Tong University, 4-20 September 2016.
- University of Muenster (WWU), 13 July 2016.
- Advances in Nonlinear Problems from Materials Science and Shape Optimization, Pisa, 27-29 June 2016.
- Scottish Partial Differential Equation Colloquium, University of Dundee, 9-10 June 2016.
- SIAM Conference on Mathematical Aspects of Materials Science, Philadelphia, 9-13 May 2016.
- University of Warwick, 10 December 2015.
- University of Nottingham, 9 December 2015.
- Mini-Workshop: Scales in Plasticity, Oberwolfach, 8-14 November 2015.
- Mathematics, mechanics and physics for tomorrow's materials, ICMS, Edinburgh, 26-30 October 2015.
- LMS Harmonic Analysis and PDEs network meeting, Edinburgh, 23 October 2015.
- University of Pavia, 28 September-2 October 2015.
- The 8th International Congress on Industrial and Applied Mathematics, Beijing, China, 10-14 August 2015.
- Intensive period on Variational Methods for Plasticity and Dislocations, SISSA, Trieste, Italy, 11-15 May 2015.
- University of Swansea, 20 March 2015.
- New perspectives in Analysis and Probability, University of Sussex, 5 March 2015.
- Imperial College, 15 January 2015.

Workshop Young Applied Analysts in the UK, University of Bath, 26-27 May 2016 (co-organised with David Bourne).

Third Scottish PDE Colloquium, University of Strathclyde, 1-2 June 2015 (co-organised with G. Barrenechea).

Workshop Young Applied Analysts in the UK, University of Glasgow, 29-30 May 2014 (co-organised with David Bourne).

- EPSRC First Grant EP/N035631/1 on "Dislocation Patterns beyond equilibrium" (£ 95699), 2016.
- London Mathematical Society, as PI (£ 4000), 2015.
- Edinburgh Mathematical Society, as PI (£ 1200), 2014.
- Carnegie Trust - Small Research Grant, as PI (£ 980), 2014.
- Glasgow Mathematical Journal Trust Fund, as PI (£ 2800), 2014.
- Edinburgh Mathematical Society, as PI (£ 1200), 2013.