Research

Preprints:

-2024: Higher-Order Reverse Isoperimetric Inequalities for Log-concave Functions, D. Langharts, F. Marín Sola,  and J. Ulivelli

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

-2024: Kubota-type formulas and supports of mixed measures, D. Hug, F. Mussnig, and J. Ulivelli

-2023: First variation of functional Wulff shapes, J. Ulivelli

-2023: Entire Monge-Ampère equations and weighted Minkowski problems, J. Ulivelli

Published/In press:

-2024: From valuations on convex bodies to convex functions, J. Knoerr and J.  Ulivelli, Mathematische Annalen

-2024: The (Self-Similar, Variational) Rolling Stones, D. Langharst and J. Ulivelli, IMRN

-2023: Convergence properties of Symmetrization processes,  J. Ulivelli, Advances in Applied Mathematics. arXiv:2207.05416 arXiv:2207.0 arXiv:2207.0541

-2021: A Generalization of Klain's Theorem to Minkowski Symmetrization of Compact sets and related topics, J. Ulivelli, Canadian Mathematical Bulletin.  

PhD Thesis:

Modern aspects of convexity and the interplay between geometry and analysis, La Sapienza, University of Rome (Italy), November 2023. 

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

Conferences/Workshops/Activities:

2024

• 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.

2023

• 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.

2022

• 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. 

2021

• 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.

Organizer: 

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

Grants: