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I obtained my degree (cum laude) in Mathematics from the University of Turin before attending a joint PhD program between the University of Turin and the Institut National Polytechnique de Lorraine. In 2008 I obtained the PhD in Mathematics from the University of Torino and the PhD in Mechanics and Energetics from the Institut National Polytechnique de Lorraine. Afterwards, I have held post-doc positions at the Universities of Torino, Padua and York, and a Marie Curie Research Fellowship at the University of York.

During my PhD I have focused on the constitutive characterization of the energy functional and stress-deformation curves of fiber-reinforced materials, in particular textiles. It is in this context that I became interested in the theory of symmetry groups and their invariants. In [15] I have applied the theory of group invariants to textiles, characterizing the deformation energy as a function of invariants that depend in a special manner on the geometrical characteristics of the warp and the weft: these results allow for the first time to distinguish the mechanical behaviour of textiles in dependence of the weave pattern and its symmetry properties.

Later, during my Post-Doc, I have started working on the applications of the theory of symmetry groups to multilattices, i.e., structures corresponding to the union of simple lattices. In this context, I have developed an algorithm, based in integer matrix theory, for the derivation and the classification of multilattices in arbitrary dimension [6]. This has different potential applications, the first of which is a software that somewhat generalizes the International Tables of Crystallography, allowing the classification of complex crystalline structures and the determination of their space groups.

More recently, I have worked, as a Marie Curie Fellow, on a research project on Mathematical Virology in collaboration with the group supervised by Prof. Twarock at YCCSA (York). The project is twofold: as a first approach, we have used techniques of high-dimensional mathematical crystallography and group theory to study the structural transitions of viral capsids with icosahedral symmetry [4-5-11-12]. In fact, icosahedral symmetry is non-crystallographic in three dimensions, and the idea was to use methods developed in the theory of quasicrystals to describe and study the transformations of sets of points approximating the viral capsid. The theory naturally lends itself to a treatment of the structural transformations of two- and three-dimensional quasicrystals, and we have applied it to study transformations of Penrose tilings of the plane [10]. As a further approach, we have also explored the possibility of describing the configurational changes of the viral capsid by coarse-grained models, that accounts for the behaviour of the proteins and their links [8] or using a Ginzburg-Landau approach based on the representation of the energy of the capsid in polynomials invariant under the icosahedral group [9].

I have also worked with a group of researchers at SISSA on a project for the identification of mechanical and assembly units of viral capsids via quasi-rigid domain decomposition. We developed and applied a general and efficient computational scheme for identification of the stable domains of a given viral capsid. The method is based on elastic network models and optimal quasi-rigid domain decomposition [7].

I have collaborated with Prof. Burkhard at the University of Connecticut, where he was leading a group of researchers that design small polypeptides capable to self-assemble into nanoparticles to be used, for instance, as synthetic vaccines or as drug targeting and delivery systems [2-3]. We developed a full classification of all possible structures that can occur as results of the assembly process, using tools of graph theory, which will aid the design and characterization of nanoparticles with desired properties.

Lately I have been working with a group at New York University and the University of Turin on the determination of possible pathways by which complex multi-body structures, such as viral capsids, destabilize, for instance during the infection process [1].

*Publications*

- Cermelli P., Indelicato G., Zappa E.,
*Minimum energy paths for conformational changes of viral Capsids.*Phys. Rev. E 96, 012407 (2017) - Indelicato G., Burkhard P., Twarock R.
*Classification of self-assembling protein nanoparticle architectures for applications in vaccine design*. R. Soc. Open Sci. DOI: 10.1098/rsos.161092 (2017) - Indelicato G., Wahome N., Ringler P., Müller S., Nieh M., Burkhard P., Twarock R..
*Principles Governing the Self-assembly of Coiled-Coil Protein Nanoparticles.*Biophysical Journal 110,(3), 646-660 (2016) Cover article for the February 2016 issue of Biophysical Journal - Salthouse DG, Indelicato G., Cermelli P., Keef T., Twarock R.,
*Approximation of virus structure by icosahedral tilings,*Acta Crystallographica A71 (4), 410-422 (2015) - Cermelli P., Indelicato G., Twarock R.,
*The role of symmetry in conformational changes of viral capsids: a mathematical approach*, Discrete and Topological Models in Molecular Biology, Eds. Jonoska N., Saito M., Natural Computing book series, Springer, 217-240 (2014) - Indelicato G.,
*An algorithm for the arithmetic classification of multilattices*, Acta Crystallographica A69, 63-74 (2013) - Polles G., Indelicato G., Potestio R., Cermelli P., Twarock R., Micheletti C.,
*Mechanical and assembly units of viral capsids identified via quasi-rigid domain decomposition*Plos Computational Biology, Vol.9, No11, e1003331 (2013). Cover article for the November 2013 issue of PLoS Comput Biol - F1000Prime recommended - Cermelli P., Indelicato G., Twarock R.,
*Non icosahedral pathways for viral capsid expansion.*Physical Review E, Vol.88, No.3 , 032710 (2013) - Zappa E., Indelicato G., Albano A, Cermelli P.,
*A Ginzburg-Landau model for the expansion of a dodecahedral viral capsid,*International Journal of Non-Linear Mechanics 56, 71-78 (2013) - Indelicato G, Keef T, Cermelli P, Salthouse D G, Twarock R, Zanzotto G.
*Structural transformations in quasicrystals induced by higher-dimensional lattice transitions*. Proceedings of the Royal Society of London. Series A, 468, 1452-1471, (2012) - Indelicato G., Twarock R.
*A Mathematical Approach To Structural Transitions In Viral Capsids.*International Journal of Modern Physics Conference Series, vol. 9, 11-23, (2012) - Indelicato G, Cermelli P, Salthouse D G, Racca S, Zanzotto G, Twarock R.
*A crystallographic approach to structural transitions in icosahedral viruses*. Journal of Mathematical Biology, vol. 64, 745-773, (2012) - Indelicato G.,
*Material symmetry and invariants for a 2D fiber-reinforced network*. Applied and Industrial Mathematics in Italy III (AIMI III), Series on advances in mathematics for applied sciences 82, 401-412, World Scientific, (2009) - Indelicato G.,
*The influence of the twist of individual fibers in 2D fibered networks.*International Journal of Solids and Structures 46 (3-4), 912-922 (2009) - Indelicato G., Albano A.,
*Symmetry properties of the elastic energy of a woven fabric with bending and twisting resistance.*Journal of Elasticity 94(1), 33-54 (2009) - Indelicato G.,
*Inextensible networks with bending and twisting effects*. Rendiconti del Seminario Matematico 65(2) 261-268 (2007)