CURRICULUM VITAE. Dr. Ilaria Lucardesi. 1 Personal data 2. 2 Education 2. 3 Grants 3. 4 Scientific interests 3

Transcription

1 CURRICULUM VITAE Dr. Ilaria Lucardesi Contents 1 Personal data 2 2 Education 2 3 Grants 3 4 Scientific interests 3 5 Publications and works Published papers Preprints Other works Research activity Compliance optimization for thin elastic structures, cf. [1], [4] A non standard free boundary problem in the plane, cf. [2] Shape derivatives for minima of integral functionals, cf. [3], [5] Fracture dynamics, cf. [6] Dislocations, cf. [7] Invited talks and seminars 9 8 Conferences and workshops attended without communication 11 9 Teaching activity Teacher in courses - CM Teaching assistant - TD & TP Tutoring Other Scientific divulgation Personal skills 13 1

2 1 Personal data Ilaria Lucardesi, born on 17/12/1985 in Bergamo (Italy), Italian nationality. Current position: postdoctoral fellow at SISSA - International School for Advanced Studies Via Bonomea 265, Trieste Italy Mobile: (+39) , lucardes@sissa.it Web page: French version of my CV: 2 Education sept Postdoctoral fellow at SISSA of Trieste (Italy) funded by the ERC advanced grant Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture (p.i. G. Dal Maso) Participation to the selection procedure for a position of Maître de Conférences in France, Section CNU 26 In 2015: shortlisted at Montpellier, 6th position In 2014: shortlisted at Marseille (LMA), 2nd position; Limoge (XLIM), 5th position; Grenoble (LJK), 6th position 2013/2014 ATER (Attaché temporaire d enseignement et de recherche), fixed-term contract for research and teaching activity, Université de Toulon (France), Lab. IMATH feb Qualification aux fonctions de Maître de conférences, Section CNU 26 qualification for the access to selection procedures for Research Professors in Applied Mathematics in France 26/02/2013 Ph.D. in Mathematical Models and Methods for Engineering (and title of Doctor Europaeus ), Politecnico di Milano (Italy) and Université de Toulon (France), joint Ph.D. thesis title: Compliance optimization for thin elastic structures; doctoral distinction: con merito - très Honorable; advisors: prof. I. Fragalà (Milano-Politecnico), prof. G. Bouchitté (Toulon); referees: prof. A. Henrot (Nancy), prof. B. Schweizer (Dortmund); committee: - prof. G. Alberti (Pisa, president), - prof. G. Bouchitté (Toulon, advisor), - prof. A. Cellina (Milano-Bicocca, member), - prof. I. Fragalà (Milano-Politecnico, advisor), - prof. A. Henrot (Nancy, referee), - prof. E. Oudet (Grenoble, member) Joint Ph.D. program at Politecnico di Milano (Itay) -primary institution- and Université de Toulon (France) Degree (Laurea Specialistica) in Mathematics, Università di Pisa (Italy) thesis title: Posizionamento ottimo con sorgenti di segno qualsiasi, (tr.: An optimal location problem with sources having arbitrary sign) mark: 110/110 cum Laude advisor prof. G. Buttazzo, co-advisor prof. L. De Pascale 2

3 Bachelor s degree (Laurea Triennale) in Mathematics, Università di Pisa (Italy) thesis title: Alcune proprietà delle onde iperboliche, (tr: Some properties of hyperbolic waves), mark: 110/110 cum Laude advisor prof. V. Georgiev, co-advisor dr. N. Visciglia june 2003 First Certificate in English (FCE), level B Baccalauréat, Scientific high school Galileo Galilei, Caravaggio (Italy) mark: 100/100 3 Grants 2450 e: INdAM - GNAMPA project 2015, funded by the Italian research group of Mathematical Analysis, Probability and their Applications, title of the project: Critical Phenomena in the Mechanics of Materials: a Variational Approach, research group: M. Bonacini and F. Iurlano (post-doc in Bonn, Germany); E. Davoli (post-doc in Vienna, Austria); I. Lucardesi, M. Morandotti, and D. Zucco (post-doc at SISSA in Trieste, Italy); R. Scala (post-doc at WIAS in Berlin, Germany); 4500 e: Vinci program 2010, scholarship for international mobility for joint Ph.D. programs between Italy and France, financed by the French-Italian University; 4000 e: INdAM scholarship, a.y. 2004/2005, fund assigned by the Italian institution INdAM to undergraduate students in Mathematics after an exam at national level. 4 Scientific interests My research interests focus on Calculus if Variations and Partial Differential Equations. In particular, I deal with fracture dynamics and dislocations; optimization in thin elastic structures; dimension reduction problems; shape optimization; shape derivatives. For a brief description of these topics, I refer to the Section Research activity. 5 Publications and works 5.1 Published papers [1] G. Bouchitté, I. Fragalà, I. Lucardesi, P. Seppecher: Optimal thin torsion rods and Cheeger sets, SIAM J. Math. Anal., 44 (1), , (2012), DOI: / [2] J.J. Alibert, G. Bouchitté, I. Fragalà, I. Lucardesi: A non standard free boundary problem arising in the shape optimization of thin torsion rods, Interfaces and Free Boundaries, 15 (1), , (2013), DOI: /IFB/296 3

4 rank=4 [3] G. Bouchitté, I. Fragalà, I. Lucardesi: Shape derivatives for minima of integral functionals, Math. Program., Ser. B, (2013), DOI /s [4] I. Lucardesi: Concentration phenomena in the optimal design of thin rods, Journal of Convex Analysis 22 (2), , (2015). [5] G. Bouchitté, I. Fragalà, I. Lucardesi: A variational method for second order shape derivatives. To appear on SICON, (2016) Preprints [6] G. Dal Maso, I. Lucardesi: The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data. Preprint SISSA 47/2015/MATE. [7] I. Lucardesi, M. Morandotti, R. Scala, D. Zucco: Optimal location of dislocations in a crystal with prescribed external strain. Preprint. 5.3 Other works [8] G. Bouchitté, I. Fragalà, I. Lucardesi: Compliance optimization with respect to the load. In preparation. [9] I. Lucardesi: Compliance optimization for thin elastic structures, Ph.D. thesis (2013). [10] translation from Italian to English of the scientific textbook Elements of Advanced Mathematical Analysis for Physics and Engineering (original title Elementi di Analisi Superiore per la Fisica e l Ingegneria ); authors A. Ferrero, F. Gazzola M. Zanotti; editor Società Editrice Esculapio-Bologna (2013). 6 Research activity The topics of my research, developed from the beginning of my Ph.D. program up to now, are briefly presented in the next paragraphs. The numerical bibliographical references correspond to my papers and works, listed in the previous section. 6.1 Compliance optimization for thin elastic structures, cf. [1], [4] Let Q be a bounded domain in R 3 and F H 1 (Q; R 3 ) be an external load. Given an isotropic elastic material which occupies a subset Ω of the design region Q, its resistance to the load F can be measured by computing a shape functional, the compliance, evaluated at the reference configuration Ω: the smaller is the compliance, the higher is the resistance. The classical problem consists in minimizing the compliance under a volume constraint (see e.g. [Allaire, 2000)]). The problem we treat is an interesting variant of the classical one: we want to find the most robust configurations, when an infinitesimal amount of elastic material is subjected to a fixed force, and is contained within a region having infinitesimal volume. Therefore, we need to perform a double limit process: on one hand we study the minimum problem when the design region is a cylinder with infinitesimal cross section, keeping fixed the volume fraction (ratio between the volume of the 4

5 elastic material and that of the design); on the other hand, we let the relative volume tend to zero. The study finds its motivation in engineering problems: for their small weight, ease of fabrication and transport, thin structures are very convenient to be used in applications. As it happens in the classical case, the problem is in general ill-posed, due to the occurrence of homogenization phenomena which prevent the existence of an optimal domain. Therefore, one of the first steps of the study is relaxation: we need to enlarge the class of admissible materials, passing from real materials, represented by characteristic functions 1 Ω : Q {0, 1} which equal 1 in presence of material and 0 otherwise, to composite materials, described by bounded functions θ : Q [0, 1] which take the value 1 in presence of material, 0 in absence of material, and an intermediate value in the homogenized regions. A priori, after the first limit procedure, an optimal structure is described by a density θ; the natural question whether θ is a characteristic function or not, namely whether the optimal structure (in the thin design, with prescribed relative volume) is a real material rather than a composite, is addressed in [2]. A more detailed description and a deeper analysis of the problem is postponed to the next paragraph. The approach we adopt draws inspiration from a recent work by I. Fragalà, G. Bouchitté and P. Seppecher, in which the authors deal with the case of thin elastic plates [Bouchitté-Fragalà-Seppecher, 2011]. These two problems are not merely technical variants one of the other, due to the substantial difference between the limit passages 3d-1d and 3d-2d, namely from 3 to 1 and from 3 to 2 dimensions. We point out that the dimension reduction process is performed without making any topological assumption on the set Ω occupied by the material. Therefore, it is not covered by the very extensive literature on 3d 1d analysis. The asymptotic analysis that we carry out is detailed in [1]. Here we just mention a surprising final result: when the load is purely torsional and the cross section of the rod is convex, the optimal configuration after the double passage to the limit is unique and can be explicitly determined as a measure, which concentrates, section by section, on the boundary of the Cheeger set of the section itself. To the best of our knowledge, until now, there was no rigorous statement and proof for this geometric characterization of optimal light torsion rods in terms of Cheeger sets. Let us emphasize that such characterization is valid only in pure torsion regime: for more general loads, due to the interplay between the bending, twisting and stretching energies, we obtain a more complicated model, where optimal measures turn out to be linked to new variants of the Cheeger problem. These last results and generalizations are gathered in [4]. 6.2 A non standard free boundary problem in the plane, cf. [2] Given a bounded domain D R 2 and a real parameter s, we consider the variational problem { } m(s) := inf ϕ( u) : u Hc 1 (D), u = s, (1) R 2 R 2 where the integrand ϕ is a convex but non-strictly convex function, defined as { y 2 ϕ(y) := if y 1 y if y < 1, and H 1 c (D) denotes the space of H 1 functions that are constant outside D (notice that if D is simply connected, the space H 1 c (D) coincides with the usual Sobolev space H 1 0 (D)). We are interested in establishing the existence of a solution u to m(s) whose gradient avoids the region of non-strict convexity of ϕ, namely such that u {0} (1, + ) a.e. in D. We call such solution special and we define its plateau as the union of the bounded connected components Ω(u) of the set { u = 0}. This problem arises from the shape optimization problem described in the previous paragraph, D being the cross section of the thin torsion rod, s being proportional to the filling ratio: in pure torsion regime, the optimal configurations of material have support, section by section, in the region 5

6 { u > 0} (in other words, the plateau corresponds to the absence of material). Moreover, in the intermediate region {0 < u < 1}, possibly negligible as it happens in the case of special solutions, composite structures appear. Hence, the analysis of m(s) can be applied to study the influence of the section s shape and of the filling ratio on the presence of homogenization regions in optimal thin torsion rods. In the analysis of the problem, the value of the parameter s and the geometry of the domain D play an important role. If D is a disc or an annulus, through explicit computations and exploiting optimality conditions, we show that m(s) admits a special solution, and we prove that there is no other solution. Moreover, we exhibit another domain, different from the previous radially symmetric ones, for which m(s) admits a special solution. After providing some elementary properties about the sign and support of generic solutions, we obtain some qulitative properties of special solutions, when the latter exist. The study of special solutions leads to the following non standard free boundary problem with a gradient obstacle: if u is a special solution, then it solves u = λ, u > 1 in D \ Ω(u) u = 1 on Γ(u) (2) u = c i on γ i, where Γ(u) := Ω(u) D is the free boundary and γ i denote the connected components of Γ(u). The characterization of the pairs (domain D-parameter s) for which m(s) admits a special solution is by now open, as well as a counterexample to special solutions. Our results, contained in the paper [2], give just a partial answer to the question. 6.3 Shape derivatives for minima of integral functionals, cf. [3], [5] The theory of shape derivatives is a widely studied topic, with many applications in variational problems and optimal design. Its origin can be traced back to the first half of the last century, with the pioneering work [Hadamard, 1968]. In recent years, the subject has received a renewed interest, partly motivated by the impulse given by the development of the field of numerical analysis in the research of optimal shapes. We deal with the shape derivative of functionals which are obtained by minimizing a classical integral of the Calculus of Variations, under Dirichlet or Neumann conditions. Namely, we consider the following functionals: { } [ ] J(Ω) := inf f( u) + g(u) dx : u W 1,p 0 (Ω), (3) Ω with Ω varying among open bounded subsets of R n with Lipschitz boundary, f : R n R and g : R R two given continuous and convex functions, satisfying growth conditions of order p and q, respectively. Similarly, we treat the Neumann case, where no boundary condition is prescribed for the admissible functions of (3). Given a vector field V of class C 1 (R n ; R n ), we consider the one-parameter family of domains which are obtained as deformations of Ω with V as initial velocity, that is we set { } Ω ε := x + εv (x) : x Ω, ε > 0. By definition, the shape derivative of J at Ω in direction V, if it exists, is given by the limit J J(Ω ε ) J(Ω) (Ω, V ) := lim. (4) ε 0 + ε The approach we adopt is different from the one usually employed in the literature, and seems to have a twofold interest: on one hand it allows to obtain the shape derivative for more general integrands f and g; on the other hand, it leads to establish conservation laws for solutions to (3). For a detailed presentation of the classical method, we refer to the recent monograph [Henrot-Pierre, 2005] and the 6

7 references therein. Our approach is based on the combined use of Convex Analysis and Γ-convergence. In particular, we heavily exploit the dual formulation of J(Ω), which in the Dirichlet case reads { } J (Ω)=inf [f (σ) + g (div σ)]dx : σ L p (Ω; R n ), div σ L q (Ω) Ω where f and g denote the Fenchel conjugates of f and g, respectively. In the Neumann case, the admissible fields σ satisfy the extra condition of zero normal trace σ n = 0 on Ω. Under our assumptions (which are weaker than the ones considered classically) we prove that the shape derivative exists. In a more regular setting, the derivative proves to be linear with respect to the deformation field V ; more precisely, it can be written as a boundary integral which depends linearly on the normal component of V on Ω. Eventually, we derive a (not widely known) necessary condition of optimality for solutions to the variational problem J(Ω). For brevity, here we write only the outcome in the regular case (but an analogous formula holds true also in general): for every solution u to J(Ω), we have ( ) div u f( u) [f( u) + g(u)] I = 0 (5) in the sense of distributions. This relation is the n-dimensional version of the well known conservation law u f (u ) [f(u ) + g(u)] = c, which is obtained as a first integral of the Euler-Lagrange equations for smooth Lagrangians (autonomous case). The results are contained in the paper[3]. This new approach can be successfully extended to compute second order shape derivatives: under stronger regularity assumptions on the continuity and convexity of the integrands, we prove existence and we provide a representation formula; furthermore, as an application, we compute the second order shape derivative of the p-torsion functional, when p 2. These results are gathered in [5]. 6.4 Fracture dynamics, cf. [6] The literature on crack propagation is very wide and in the last twenty years has received a renewed interest (see e.g. [Ambrosio-Braides, 1995; Francfort-Marigo, 1998; Bourdin, 2008]). The first models proposed can be enclosed in the quasi static theory: the external force f, which is responsible of the origin and evolution of the fracture, is assumed to vary more slowly than the velocity of the elastic response u of the material (cf. [Francfort-Larsen, 2003; Dal Maso-Francfort-Toader, 2005]). Therefore, at each instant t, u(t) is the elastic equilibrium associated to the forcing term f(t). This model favors the numerical implementation, based on the Ambrosio-Tortorelli approximation (cf. [Bourdin-Francfort- Marigo, 2007; Artina et al., 2015]). The analysis of dynamic evolution has several open aspects, starting from the choice of an appropriate model. However, a reasonable theory should contain some general principles: i) irreversibility: the crack set Γ(t) Ω is increasingin time, being Ω R n the region occupied by the material; ii) elastodynamics off of the crack: in Ω(t) := Ω\Γ(t) the material undergoes an elastic deformation u : Ω(t) R (antiplane case), which satisfies, in some suitable weak sense, the equation ü(t) u(t) = f(t) in Ω(t), supplemented by a Dirichlet boundary condition w(t) on a portion of the boundary D Ω, and homogeneous Neumann boundary conditions on N Ω := Ω \ D Ω and on the crack Γ(t); iii) energy-dissipation balance: at every time, the kinetic+elastic energy of u(t) and the total work done by the load are balanced by the energy dissipated by the crack Γ(t), which is, in the Griffith theory [Freund, 1990], proportional to the crack surface increment; 7

8 iv) selection principle: among the pairs (Γ(t), u(t)) satisfying the properties above, there should be a principle which predicts the right crack propagation, preventing stationary cracks to be always the solution. Finding the unknowns Γ(t) and u(t) is a very difficult task. Therefore, as a preliminary step, in [6] we address the question of existence and uniqueness of solutions to the wave equation in (ii), when the fracture grows on a C 2 manifold of dimension n 1, assuming to know a priori the crack position at every time. The main issue here is the fact that the boundary Ω(t) is not regular, due to the presence of the crack Γ(t) (for the regular case see, e.g. [Cooper, 1975; Sikorav, 1990]). A notion of solution in a domain with a growing crack was introduced in [Dal Maso-Larsen, 2011], in the case of homogeneous Neumann conditions on the whole boundary of Ω(t) and under much weaker assumptions on the growing cracks. In the same paper, Dal Maso and Larsen prove the existence of solutions, with the minimizing movements approach. The method we apply is different, and relies on a change of variables: transforming the domain {(t, x) (0, T ) Ω : x Ω(t)} into the cylinder (0, T ) Ω(0), we are led to study v(t, y) div y (B(t, y) y v(t, y)) + a(t, y) y v(t, y) 2b(t, y) y v(t, y) = g(t, y) (6) for t [0, T ] and y Ω(0), with Dirichlet-Neumann boundary conditions on Ω, and homogeneous Neumann conditions on the fixed crack Γ(0). In the new setting, we obtain existence, uniqueness, and continuous dependence on the data, of the solution v of (6). These results translate into existence, uniqueness, and continuous dependence on the cracks Γ(t), of the solution u of the original problem. We expect that the continuous dependence of u with respect to the family {Γ(t)} t will be an important tool for a precise mathematical formulation of a dynamic model of crack evolution, in the spirit of [Larsen, 2010]. 6.5 Dislocations, cf. [7] Dislocations are point defects appearing in crystals, and explain the observation of plastic deformations. Due to the mechanical applications, the literatute on this topic is very wide (see, for instance, [Cermelli- Leoni, 2005; Blass et al., 2015; Conti et al. 2015]). We focus our attention on an unexplored aspect: find the optimal position of screw dislocations in a material. To this purpose, we consider suitable boundary conditions on the crystal, which prevent dislocations to migrate to the boundary and leave the domain, as it happens in the classical setting. The study involves optimization techniques and Γ-convergence, and relies on the so-called core radius approach (see, e.g., [Cermelli-Gurtin, 1999]): in order to apply variational techniques, we compute the elastic energy stored far from dislocations, namely we remove small discs of radius ε around the defects. The small parameter ε represents the lattice spacing which, in the second part of the study, is sent to zero. The results are contained in the paper in preparation [7]. Bibliography - G. Allaire: Shape optimization by the homogenization method. Springer, Berlin (2002). - L. Ambrosio, A. Braides: Energies in SBV and variational models in fracture mechanics, Homogenization and applications to material sciences (Nice), GAKUTO Internat. Ser. Math. Sci. Appl. 9, Gakkotosho, Tokyo (1995), M. Artina, M. Fornasier, S. Micheletti, S. Perotto: Anisotropic mesh adaptation for crack detection in brittle materials., SIAM J. Sci. Comput. 37 no. 4 (2015), B633 B T. Blass, I. Fonseca, G. Leoni, M. Morandotti: Dynamics for systems of screw dislocations, SIAM J. Appl. Math. 75 no. 2 (2015), G. Bouchitté, I. Fragalà, P. Seppecher: Structural optimization of thin plates: the three dimensional approach, Arch. Ration. Mech. Anal. 202 no. 3 (2011), B. Bourdin: The variational approach to fracture. J. Elasticity 91 (2008),

9 - B. Bourdin, G.A. Francfort, J.J. Marigo: Numerical implementation of the variational formulation for quasistatic brittle fracture, Interfaces and Free Boundaries 9 (2007), P. Cermelli, M.E. Gurtin: The motion of screw dislocations in crystalline materials undergoing antiplane shear: glide, cross-slip, fine cross-slip, Arch. Rat. Mech. Anal. 148 (1999), P. Cermelli, G. Leoni: Renormalized energy and forces on dislocations, SIAM J. Math. Anal. 37 (2005), S. Conti, A. Garroni, M. Ortiz: The line-tension approximation as the dilute limit of linear-elastic dislocations, submitted (2015). - C. Cooper: Local decay of solutions of the wave equation in the exterior of a moving body, J. Math. Anal. Appl. 49 (1975), G. Dal Maso, G.A. Francfort, R. Toader: Quasistatic crack growth in nonlinear elasticity, Arch. Ration. Mech. Anal. 176 no. 2 (2005), G. Dal Maso, C.J. Larsen: Existence for wave equations on domains with arbitrary growing cracks, Rend. Lincei Mat. Appl. 22 (2011), G.A. Francfort, C.J. Larsen: Existence and convergence for quasi-static evolution in brittle fracture, Comm. Pure Appl. Math. 56 no. 10 (2003), G.A. Francfort, J.-J. Marigo: Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids 46 no. 8 (1998), L.B. Freund: Dynamic Fracture Mechanics, Cambridge University Press (1990). - J. Hadamard: Mémoire sur le problème d analyse relatif à l équilibre des plaques élastiques encastrées, Oeuvres de J. Hadamard, CNRS Paris (1968). - A. Henrot, M. Pierre: Variation et Optimisation de Formes. Une Analyse Géométrique. Mathématiques & Applications 48, Springer Berlin (2005). - C.J. Larsen: Models for dynamic fracture based on Griffith s criterion, IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, ed. K. Hackl, IUTAM Bookseries 21 (2010), J. Sikorav: A linear wave equation in a time-dependent domain, J. Math. Anal. Appl. 153 no. 2 (1990), Invited talks and seminars (forthcoming) - Optimal location of dislocations in a crystal with prescribed external strain, 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session Advances in the mathematical modeling of failure phenomena and interfaces in materials, Orlando FL (USA), 1-5/07/2016; (forthcoming) - Locating one dislocation, Univ. J. Fourier, Grenoble (France), 24/03/2016; (forthcoming) - Do optimal thin torsion rods contain homogenized regions? (France), 22/03/2016; École des Mines, Nancy (forthcoming) - Locating one dislocation, Rencontre ANR Geometrya & Optiform, ENS Paris (France), 17-18/03/2016; Do optimal thin torsion rods contain homogenized regions? Variational Perspectives, Politecnico di Torino (Italy), 08/03/2016; Do optimal thin torsion rods contain homogenized regions? CMAP, École Polytechnique, Palaiseau (France), 23/02/2016; Do optimal thin torsion rods contain homogenized regions? Analysis Junior Seminars, SISSA, Trieste (Italy), 05/02/2016; The wave equation on domains with cracks growing on a prescribed path, XXII Convegno Nazionale di Calcolo delle Variazioni, CIRM Trento, Levico Terme (Italy), 18-22/01/2016; 9

10 The wave equation on domains with cracks growing on a prescribed path, Politecnico di Milano (Italy), 15/01/2016; The wave equation on domains with cracks growing on a prescribed path (poster session), International workshop on Calculus of Variations and its Applications, Lisbon (Portugal), 16-19/12/2015; The wave equation on domains with cracks growing on a prescribed path, Università di Pisa (Italy), 03/12/2015; Shape derivatives for minima of integral functionals, workshop PDEs, Optimal Design and Numerics, Centro de Ciencias de Benasque Pedro Pascual (Spain), august 23rd - september 4th 2015; The wave equation on domains with cracks growing on a prescribed path, workshop Trends in Nonlinear Analysis 2015, SISSA of Trieste (Italy), 1-3/07/2015; An introduction to Convex Analysis and an application in shape optimization, SISSA of Trieste (Italy), 21/11/2014; Dérivées de forme pour minima de fonctionnelles intégrales, Univ. de Limoges (France), Laboratoire XLIM, april 2014; Design optimal de poutre en flexion + torsion : phénomènes de concentration, working group in PDEs and Calculus of Variations, Frumam Marseille (France), april 2014; Dérivées de forme pour minima de fonctionnelles intégrales, Journées Nice-Toulon-Marseille, Île de Porquerolles (France), june 2013; Γ-convergence: theory and applications, Politecnico di Milano (Italy), april 2012; A non standard free boundary problem arising in shape optimization of thin torsion rods, Université de Toulon (France), february 2012; A non standard free boundary problem arising in shape optimization of thin torsion rods, XXII Convegno Nazionale di Calcolo delle Variazioni, CIRM Trento, Levico Terme (Italy), february 2012; A non standard free boundary problem arising in shape optimization of thin torsion rods, Politecnico di Milano, november 2011; Théorème de Hopf et ses variantes, Summer school on Calculus of Variations (junior session), CIRM Luminy (France), july 2011; An introduction to optimal transportation theory, Politecnico di Milano (Italy), march The slides of my talks are available on my web page 10

11 8 Conferences and workshops attended without communication Winter School on Calculus of Variations in Physics and Materials Science Institute for Mathematics University of Würzburg (Germany), february 2016; Eighth Summer School in Analysis and Applied Mathematics, Università di Roma La Sapienza (Italy), june 2015; Variational Methods for Plasticity and Dislocations, intensive trimester, SISSA of Trieste (Italy), february-may 2015; XXV Convegno Nazionale di Calcolo delle Variazioni, CIRM Trento, Levico Terme (Italy), february 2015; Advances and Perspectives in the Calculus of Variations, SISSA, Trieste (Italy), december 2015; Variational Modeling in Solid Mechanics, Università di Udine, september 2014; Trends in Non Linear Analysis, IST - Lisbona (Portugal), july 2014; Calculus of Variations and Optimization, A conference to celebrate the 60th birthday of Giuseppe Buttazzo, Pisa (Italy), may 2014; Journées NTM, Île de Porquerolles (France), may 2014; XXIV Convegno Nazionale di Calcolo delle Variazioni, CIRM Trento, Levico Terme (Italy), january 2014; Rencontre ANR Geometrya, Marseille (France), november 2013; Nonlinear elliptic and parapolic PDEs, Politecnico di Milano (Italy), june 2013; New trends in shape optimization, Centro Ennio de Giorgi, Pisa (Italy), july 2012; Journées NTM, Île de Porquerolles (France), june 2012; Aspects in Nonlinear PDEs, Politecnico di Milano (Italy), september 2011; XXI Convegno Nazionale di Calcolo delle Variazioni, CIRM Trento, Levico Terme (Italy), february 2011; XX Convegno Nazionale di Calcolo delle Variazioni, CIRM Trento, Levico Terme (Italy), february 2010; Summer school in Calculus of Variations and Optimal Transportation Theory, Université de Grenoble (France), july Teaching activity For brevity, in the following I will refer to the undergraduate students level simply by specifying their year of study. Both in Italy and France, the university course of study lasts five years. 9.1 Teacher in courses - CM Theory of Γ-convergence and its applications (2010/2011 and 2011/2012, 2h + 4h ) Lecture notes included in the course of Calculus of Variations 5th year undergraduate students and Ph.D. students of Mathematical Engineering, Politecnico di Milano (Italy) 11

12 9.2 Teaching assistant - TD & TP An introduction to PDEs (1st sem. 2014/2015, 6h) 5th year undergraduates students and Ph.D. students in Mathematics, SISSA of Trieste (Italy) Content: heat equation and wave equation. Analyse 3 (2nd sem. 2013/2014, 21h) 2nd year undergraduates students of Mathematics, Univ. Toulon (France) Content: number and function series; convergences; Fourier series; generalized and improper integrals; comparison integral-series. Mécanique (2nd sem. 2013/2014, 6h + 6h, computer lab.) 1st year undergraduates students of Mathematics, Physics and Chemistry, Univ. Toulon (France) Content: Mechanics - static part. Probabilités et statistiques descriptives (1st sem. 2013/2014, 30h) 2nd year undergraduates students of Applied Math. to Social Sciences, Univ. Toulon (France) Content: discrete probabilities, discrete and continuous random variables, usual probability laws, approximations and law of large numbers. Méthodes de calcul statistique (1st sem. 2013/2014, 21h) 1st year undergraduates students of Applied Math. to Social Sciences, Univ. Toulon (France) Content: descriptive statistics, dispersion parameters of a random variable, statistical distributions of multiple variables, relation with random variables in Probability. Statistiques (1st sem. 2013/2014, 12h) 2nd year undergraduates students of Biology, Univ. Toulon (France) Content: elements of combinatory, probability, discrete and continuous random variables, classic laws, asymptotical laws. Complementi di Matematica (2nd sem. 2012/2013 and 2nd sem. 2011/2012, 24h + 24 h) 1st year undergraduates students of Computer Science, Univ. Milano-Bicocca (Italy) Content: complex numbers, vector spaces, homomorphisms, matrices, systems of linear equations, ODE, elements of calculus in several variables. Complementi di Analisi Matematica (1st sem. 2010/2011, 30h) 4th year undergraduates students of Chemical Engineering, Politecnico di Milano (Italy) Content: elements of functional analysis, integral transformations, solution of ODEs and PDEs. 9.3 Tutoring reading course (2nd sem. 2015/2016) 1st year PhD students in Applied Mathematics, SISSA of Trieste (Italy) Content: basic functional analysis, L p spaces, Banach and Hilbert spaces. 12

13 9.4 Other substitute teacher of Mathematics and Physics (february-march 2013, 40h) high school Liceo don Milani, Romano di Lombardia (Italy) volunteer in the school SMaC of Trieste ( devoted to help the minors who have abandoned their studies to get their diploma. I teach the part concerning plane geometry. 10 Scientific divulgation Since the beginning of my post-doc, I have taken part of the project of scientific divulgation SISSA for school promoted by my institution, organizing the following activities: Parsimonious Nature: interactive seminar about theoretical end experimental solution (soap films) of maximum/minimum problems with constraint; Searchers find....what about re-searchers?: orientation seminar for high school students; Geometric construction of numbers: ruler and compass VS origami: interactive lesson for middle school students. Moreover, as a member of the non-profit cultural Association Aeolipile, I have organized the following public events, held in Pisa (Italy): Math face to face: 3 days for discovering Math, through an interactive exhibition, games, and seminars, may 2012; 10 9: a journey towards the infinitesimals: 2 evenings talk + discussion + happy hour about nanotechnologies, december 2011; 2011: Chemistry Odyssey: 3 days to celebrate the International Year of Chemistry, through interactive exhibitions, laboratories and conferences, may Personal skills Organizing skills: - co-organizer of the Calcvar seminars (seminars of Calculus of Variations) of SISSA (Italy); - co-organizer (together with Dr. M. Morandotti) of the Mini-symposium Dislocations: recent results and perspectives, to be held during the 7th European Congress of Mathematics; july, TU Berlin, Germany; - candidate p.i. in the project Variational analysis of failure phenomena and interfaces in the mechanics of materials, presented last february for the yearly selection of projects funded by the Italian research group of Mathematical Analysis, Probability and their Applications (results available at the end of march 2016); research group: M. Bonacini (post-doc in Bonn, Germany), E. Davoli (post-doc in Vienna, Austria), F. Iurlano (post-doc in Bonn, Gernamy), M. Morandotti (post-doc at SISSA in Trieste, Italy), P. Piovano (post-doc in Vienna, Austria), R. Scala (post-doc at WIAS in Berlin, Germany); - as a member of a non-profit cultural Association, organizer of public events of scientific divulgation. Technical skills: - excellent knowledge of Asymptote, L A TEX and Beamer; 13

14 - knowledge of FreeFem ++, Mathematica, and Matlab; - knowledge of programming languages Pascal, C and Fortran; Languages: - Italian: mother tongue; - English: level C1; - French: level B1. 14