Edoardo Cavallotto
Ph.D. student @ Université Paris-Sud (PSUD)
since 10/1/2014 for 3 years.
under the supervision of Prof. Guy David
Research
The subject of my research is the Plateau problem in some of its variants. There are many of them but the general idea is the following: given a boundary set B, one tries to minimize the area of a set E bounded by B. Part of the problem is hidden in the choice of a suitable definition of “area” and “bounded by”. In particular we are interested in a formalisation, similar to the Almgren's one, where the area is the Hausdorff measure and the boundary condition is expressed in terms of a one parameter family of deformation. We are concerned in the existence of minimisers (a property that is still widely unknown both in Almgren's and in size minimizing current framework) as well as in minimiser's (and, in general, almost minimiser's) regularity properties, in particular near the boundary, another question that has not been investigated very much. We also focused on a slight variant of the problem called “sliding boundary”. In this new setting, after fixing a set L, we only consider those modifications f such that f(x) sits in L whenever x belongs to L, and the functional we want to minimise is modified on L by multiplying the Hausdorff area by a parameter 0
Local training activities:
- [Course] Complex geometry and Hodge groups (lecturer L. Charles) - a.a. 2014-2015 Paris, France
- [Course] Differential topology (lecturer A. Zorich) - a.a. 2014-2015 Paris, France
- [Course] Rectifiability and currents (lecturer T. De Pauw) - a.a. 2014-2015 Paris, France
Network-wide training activities:
- [Workshop] Geometric measure theory and calculus of variations - June 15 to July 4, 2015 Grenoble, France
- [Workshop] Analysis and Geometry in metric spaces - June 1-5, 2015 Madrid, Spain
- [Summer School] Calculus of Variation, Optimal transportation and Geometric Measure Theory - June 27 to July 15, 2016 Lyon, France
- [Workshop] A mathematical tribute to Ennio De Giorgi - September 19-23, 2016 Pisa, Italy
- [Conference] Harmonic Analysis Program - February 1, 2017 Berkeley, United States
- [Workshop] Harmonic Analysis Program - January 17 to May 26, 2017 Berkeley, United States
- [Conference] Harmonic Analysis and Geometric Measure Theory - October 2, 2017 Marseille, France
Outreach:
- [Course] Analyse Mathématique - a.a. 2014-2015 Paris, France
- [Workshop] Journée de rentrée - a.a. 2014-2015 Paris, France
- [Workshop] Fête de la science à l'Université Paris-Sud - October 7-11, 2015 Paris, France
- [Course] Analysis I - 2017 Spring PSUD, Paris, France
- [Course] LInear Algebra - 2017 Spring PSUD, Paris, France
- [Course] Complements of Analysis - 2017 Spring PSUD, Paris, France
Talks and Poster Presentations:
- [Talk] Cones Minimaux et Calibrations at Séminaire Périodique d'analyse harmonique d'Orsay - a.a. 2014-2015 Paris, France
- [Talk] Minimal Cones and Calibrations at Mid-term Review Meeting - December 9, 2015 Helsinki, Finland
- [Talk] Minimal Cones and Calibrations at Séminaire doctorant en 2° année - March 17, 2016 Paris, France
- [Talk] Minimal boundary cones at MAnET Metric Analysis Meeting - January 18-19, 2017 Paris, France
- [Talk] Minimal boundary cones at ANT&HA Graduate Student Seminar - February 14,2017 Berkeley, United States
- [Talk] Sobolev spaces on metric measure spaces at Harmonic Analysis Graduate Student - March 15,2017 Berkeley, United States
- [Talk] Cônes minimaux et calibrations at Seminaire des doctorants d'Orsay - May 21, 2017 Paris
- [Talk] Minimal boundary cones at Seminari d'anàlisi de Barcelona - September 18, 2017 Barcelona
- [Talk] Sliding boundary cones at Sub-Riemannian Geometry Harmonic Analysis, PDE and Applications - January 24-27, 2018 Bologna, Italy
Secondment:
- UAB - June 6 to September 30, 2017 Barcelona, Spain
Publications and Preprints
- E. Cavallotto, Minimal cones and calibrations report
- E. Cavallotto, Minimal boundary cones report
- E. Cavallotto, Sliding boundary cones report
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