Luigi Ambrosio is Full Professor of Mathematical Analysis at Scuola Normale Superiore of Pisa since 1997. In 2019 he has been nominated Director of Scuola Normale Superiore. Prof. Ambrosio is a long term visiting scientist in the Max Planck Institute of Leipzig, the Massachusetts Institute of Technology, the ETH of Zurich, and the Institute Henri Poincaré of Paris. Prior to joining Scuola Normale Superiore, Prof. Ambrosio has been Full Professor at the University of Pisa and at the University of Benevento, both in Italy. Born in Alba, Italy, in 1965, he obtained his degree in mathematics (summa cum laude) in 1985 from the University of Pisa and started his successful career as Research Assistant at the Second University of Rome followed by a position as Associate Professor at the University of Pisa. In 2015 Prof. Ambrosio has been awarded the PhD honoris causa by the École Normale supérieure, Lyon. Prof. Ambrosio's scientific interest include the calculus of variations, the Geometric Measure Theory; the Transportation Theory and their application to partial differential equations. For his research he has been awarded numerous prizes, including which the "Riemann prize of the Riemann International Mathematics School" (2022); the Balzan Prize for the achievements in the theory of partial differential equations (2019); the Blaise Pascal Medal of the European Academy of Sciences (2019); the gold medal for achievements in Mathematics awarded by the XL National Academy of Sciences, Italy (2015). Abstract: In this talk Prof. Ambrosio will illustrate new questions, at the interface between Calculus of Variations and Geometric Measure Theory, motivated in a broad sense by the more applied machine learning community. More specifically, he will deal with second-order variational problems in the setting of functions with bounded variation and study the extremal properties of continuous and piecewise affine functions in the unit ball of a suitable energy, used as a regularization term in the applied community. In connection with this, a fine approximation result by piecewise affine function has been investigated. Papers written in collaboration with C.Brena, S.Conti, S.Aziznejad and M.Unser. The title of the Colloquium is "On some variational problems involving functions with bounded Hessian". The event will take place in the Budinich Lecture Hall on the ICTP campus. Light refreshments will be served after the talk. All are welcome to attend. The talk will also be live streamed from the ICTP website.
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