Research

Papers:

-2025: First variation of functional Wulff shapes, J. Ulivelli, Advances in Mathematics (in press).

-2024: Additive kinematic formulas for convex functions, D. Hug, F. Mussnig, and J. Ulivelli, Canadian Journal of Mathematics.

Supervisors: Gabriele Bianchi, Paolo Gronchi (University of Florence, Italy)

08/07/2025: "From bodies to functions: An overview", Current trends in Geometric Valuation theory, Erdos center, Budapest.
31/05/2025: "Between Brascamp-Lieb and Colesanti inequalities", 2025 Szeged Workshop on Convexity, Szeged.
17/02/2025: "Geometric inequalities on convex functions", Analysis and Convex Geometry Week at UniAndes , Bogota'.
06/02/2025: "Support of SO(n − 1)-invariant mixed measures and applications", analysis seminar, Charles University, Prague.

12/06/2024: "A local theory of valuations", Convex Geometry in Florence, University of Florence.
20/02/2024: "Kubota-type formulas and supports of mixed measures ", workshop "Asymptotics of (random) convex sets: fluctuations and large deviations", Hausdorff Research Institute for Mathematics, Bonn.
22/01/2024: "Poincaré inequalities on unbounded hypersurfaces", winterschool "Geometry and Probability", Poster, Hausdorff Research Institute for Mathematics, Bonn.

05/12/2023: "On mixed measures, Part II", Privatissimum, TU Wien. (Part I by Fabian Mussnig).
30/06/2023: "Entire Monge-Ampère equations and weighted Minkowski problems", INdAM Meeting, "Convex Geometry - Analytic Aspects", Cortona.
19/06/2023: "The (Self-Similar, Variational) Rolling Stones", La Sapienza, University of Roma, Seminar of Mathematical Analysis.
05/06/2023: "First variation of Wulff shapes of convex functions", CIEM-Castro Urdiales, Geometric Valuation Theory- From convex sets to functions.
17/03/2023: "Equidecomposability: From Hilbert's third problem to the theory of Valuations", MATH Talks, Sapienza University of Rome.
19/01/2023: "First variations and where to find them", Privatissimum, TU Wien.

13/10/2022: "The Log-Minkowski problem in the calculus of variations", Semester Program in Harmonic Analysis and Convexity, ICERM at Brown University, Providence RI.
06/10/2022: "Geometric approaches to functional valuations", Deane Yang and Gaoyong Zhang's research group meeting at the Courant Institute, New York University.
27/09/2022: "Valuations on convex functions with compact domain", Harmonic Analysis Methods in Geometric Tomography, ICERM at Brown University, Providence RI.
23/05/2022: "Isoperimetric inequalities for Hessian valuations", Workshop in "Convexity and High-dimensional Probability", GeorgiaTech, Atlanta.
21/04/2022: "From Convex to Hessian Valuations", Mini-symposium on "Geometric Probability and Valuation Theory", TU Wien.
31/03/2022: "From Convex to Hessian Valuations", Privatissimum, TU Wien.
18/03/2022: "The Brunn-Minkowski inequality: how to shape a crystal", MATH Talks, Sapienza University of Rome.
28/01/2022: "Convergence Properties of Symmetrization Processes", GIM seminars.

09/12/2021: "Geodesic Convexity and the Brunn-Minkowski inequality", Privatissimum, TU Wien.
30/08/2021-03/09/2021: "Generalization of Klain's Theorem to Compact Sets", CIME "Convex Geometry" (Cetraro), Poster Session.
29/04/2021: "Characterizing Converging Symmetrization Processes", Privatissimum, TU Wien.
15-19/03/2021: "Generalization of Klain's Theorem to Compact Sets", Current Trends in Convex Geometry (Bremen & Murcia). Poster Session.
22-25/02/2021: "Generalization of Klain's Theorem to Compact Sets", Münster Winterschool on Analysis and Applied Mathematics. Poster Session.

MATH Talks: Math After Thesis, advanced lectures for students. Sapienza, University of Rome (2022, 2023).

-2025/2029: FWF Principal Investigator Project, "Algebraic Integral Geometry for Convex Functions" (TU Wien).

-2022/2023: Grant "Avvio all Ricerca", Sapienza University of Rome.

-2021/2022: Grant "Avvio all Ricerca", Sapienza University of Rome.

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