Convex Geometry

Andrea Colesanti received a PhD in Mathematics at the University of Florence, where he is currently Professor in Mathematical Analysis. his main research interest is convexity, and in particular analytic aspects of convex geometry (in finite dimension). He has been interested in the connections between convex geometry and the theory of partial differential equations of elliptic type, and other areas of analysis. Together with local collaborators and colleagues from other countries, he has organized thematic workshops and schools about convex geometry. With Gabriele Bianchi and Paolo Gronchi, he has been the editor of the book Analytic Aspects of Convexity, published in the Springer INdAM.Series, in 2018.Monika Ludwig received a PhD in Mathematics at the Technische Universität Wien. She was an Erwin-Schrödinger Fellow at University College London and New York Polytechnic University and visiting professor at the University of Bern. She was a Professor at New York University before she returned to the Technische Universität Wien as a Professor of Convex and Discrete Geometry. She received the Hlawka-Prize of the Austrian Academy of Sciences and the Förderungspreis of the Austrian Mathematical Society. She became a Corresponding Member of the Austrian Academy of Sciences in 2011, a Fellow of the American Mathematical Society in 2012, and a Full Member of the Austrian Academy of Sciences in 2013. She was a plenary speaker at the European Congress of Mathematics in 2021.

• - 1. Notation and Introductory Material. - 2. Valuations on Convex Bodies and Functions. - 3. Geometric and Functional Inequalities. - 4. Dualities, Measure Concentration and Transportation. - 5. Symmetrizations.