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I begin by thanking my advisor, Alessandro Veneziani, aka {\it the boss}. Thank you because actually you were not a boss; because you shared with me your love for applied mathematics; because sometimes we did not agree; because you challenged me, studied and learned with me. Grazie perch\'e ci hai insegnato che non \`e importante giocare in panchina con la Juventus ma in campo con l'Atalanta e che non c'\`e gusto a vincere facile.

Thank you to my committee members, Michele Benzi and Jim Nagy, not only because you took time to read my thesis and provide me with advice and suggestions; thank you for being a guide during these four years. Your doors were always open for me anytime I was looking for scientific (and non-scientific) answers. 

Thank you to Eldad Haber, I have learned so much from you. You showed me that the world does not have to be discretized by finite elements and you passed on your passion for scientific computing, optimization and inverse problems. Thank you to Max Gunzburger because you got interested in my work as soon as we met and you kept on advising me whenever I needed suggestions and alternative points of view. Your brilliant and challenging ideas inspired me during this work.

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Special thanks to Tiziano and Umberto, because life(V) would not have been so easy without you. To Marina, BB, aka LucaB, and GG, aka LucaG, because life(V?) is not easy at all, but you made it fun. To N404 inhabitants and ex-inhabitants, best office mates ever. To Valen and don Pie because it was like having you here; inevitabilmente, immancabilmente ed instancabilmente presenti. To Gio and Marci because you always knew that I could have made it, even when I did not believe so; this work is dedicated to you.

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And thank you, Mauro, because all this could not have been possible without you $\heartsuit$




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