MAnET Metric Analysis for Emergent Technologies

Eugenio Vecchi

Post Doc @ Alma Mater Studiorum Università di Bologna - Dipartimento di Matematica (UNIBO)

since 10/1/2015 for 2 years.

under the supervision of Prof. Bruno Franchi

Research

During my PhD studies under the supervision of Prof. Balogh, I have worked on sub-Riemannian geometry and Geometric Analysis. My main interest has concerned curvature problems in the contest of the first Heisenberg group; in particular, I studied possible definitions of horizontal Gaussian curvature for smooth surfaces, away from characteristic points.

Local training activities:

• [Seminars] Topics in Mathematics, periodic seminar organized by F. Ferrari and A. Martinez - a.a. 2015-2016 Bologna, Italy

Network-wide training activities:

• [Workshop] Geometric Analysis on sub-Riemannian manifolds - September 29 to October 3, 2014 Paris, France
• [Workshop] Sub-Riemannian Analysis, PDE and Applications - January 26-30, 2015 Berna, Swiss
• [Workshop] Geometric Analysis in the Heisenberg group - March 4-6, 2015 Bologna, Italy
• [Summer School] Analysis and Geometry in metric spaces - July 6-10, 2015 Levico Terme, TN, Italy
• [Conference] Two-day meeting on linear and nonlinear PDE's in honor of the 65th birthday of Christian Gutiérrez - June 9-10, 2016 Bologna, Italy
• [Course] Singular phenomena and singular geometries - June 20-23, 2016 Pisa, Italy
• [Workshop] A mathematical tribute to Ennio De Giorgi - September 19-23, 2016 Pisa, Italy
• [Conference] James SERRIN: from His legacy to the new frontiers - January 30 to Februrary 2, 2017 Perugia (PG), Italy
• [Course] CIME-CIRM Course on New Trends on Analysis and Geometry in Metric Spaces (10th - June 26-30, 2017 Levico, Italy

Organization activities:

• [Conference] Sub-Riemannian Geometry Harmonic Analysis, PDE and Applications - January 24-27, 2018 Bologna, Italy

Outreach:

• [Course] Mathematical Analysis I - a.a. 2015-2016 Bologna, Italy
• [Course] Mathematical Analysis II - 2° semester 2015-2016 Bologna, Italy
• [Course] Mathematical Analysis I - a.a. 2016-2017 Bologna, Italy
• [Course] Crash course in Mathematics - 2017-2018 Fall Unibo, Bologna, Italy

Talks and Poster Presentations:

• [Talk] Gauss curvature in the Heisenberg group: a proposal at Mid-term Review Meeting - December 9, 2015 Helsinki, Finland
• [Talk] Steiner formula in the Heisenberg group at Bruno Pini Mathematical Analysis Seminar - April 7, 2016 Bologna, Italy
• [Talk] Steiner formula in the Heisenberg group at 3 days on evolution PDEs - April 27-29, 2016 Fisciano (SA), Italy
• [Talk] Bourgain-Brezis-Mironescu formula in the magnetic setting at MAnET Metric Analysis Meeting - January 18-19, 2017 Paris, France
• [Talk] Horizontal Gauss curvature in the Heisenberg group at International Conference on Elliptic and Parabolic Problems - May 22-25, 2017 Gaeta, Italy
• [Talk] Gauss curvature in the Heisenberg group via Riemannian approximation at Brescia-Trento Nonlinear Days - Edition I - May 26, 2017 Trento, Italy
• [Talk] Symmetry results for optimal pairs in the composite plate problem at EDP e DINTORNI, III Meeting around PDE - December 18, 2017 Bari, Italy
• [Talk] Symmetry results for optimal pairs in the composite plate problem at Sub-Riemannian Geometry Harmonic Analysis, PDE and Applications - January 26, 2018 Bologna, Italy

Secondment:

• Université Nice Sophia Antipolis - March10 to June 6, 2017 Nice, France

Publications and Preprints

• Z. Balogh, F. Ferrari, B. Franchi, E. Vecchi, K. Wildrick, Steiner's formula in the Heisenberg group on Nonlinear Analysis, Theory, Methods and Applications Vol 126 Elsevier Limited 2015 pp. 201-217 open access version
• Z. Balogh, J. T. Tyson, E. Vecchi, Intrinsic curvature of curves and surfaces and a Gauss-Bonnet Theorem in the Heisenberg group on Mathematische Zeitschrift Vol 287 Springer Berlin Heidelberg 2016 pp. 1-38
• H. M. Nguyen, A. Pinamonti, M. Squassina, E. Vecchi, New characterizations of magnetic Sobolev spaces on Advances in Nonlinear Analysis Walter de Gruyter GmbH 2017 pp. open access version
• A. Fiscella, A. Pinamonti, E. Vecchi, Multiplicity results for magnetic fractional problems on Journal of Differential Equations Vol 263 Elsevier Science B.V. 2017 pp. 4617-4633 open access version
• A. Pinamonti, M. Squassina, E. Vecchi, Magnetic BV functions and the Bourgain-Brezis-Mironescu formula on Advances in Calculus of Variations Walter de Gruyter GmbH 2017 pp. 1-30 open access version
• A. Pinamonti, M. Squassina, E. Vecchi, The Maz'ya-Shaposhnikova limit in the magnetic setting on Journal of Mathematical Analysis and Applications Vol 449 Elsevier 2017 pp. 1152-1159 open access version
• F. Ferrari, E. Vecchi, Hoelder behavior of viscosity solutions of some fully nonlinear equations in the Heisenberg group preprint
• F. Colasuonno, E. Vecchi, Symmetry in the composite plate problem preprint
• E. Vecchi, Gauss curvature in the Heisenberg group: a proposal report
• E. Vecchi, Bourgain-Brezis-Mironescu formula in the magnetic setting report
• E. Vecchi, Symmetry results for optimal pairs in the composite plate problem report