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
Complementary training activities:
- Workshop on Analysis and Geometry in metric spaces - June 1-5, 2015 Madrid, Spain
- Geometric measure theory and calculus of variations - June 15 to July 4, 2015 Grenoble, France
Local training activities:
- Complex geometry and Hodge groups (lecturer L. Charles) - A.A 2014/15 Paris, France
- Differential topology (lecturer A. Zorich) - A.A 2014/15 Paris, France
- Rectifiability and currents (lecturer T. De Pauw) - A.A 2014/15 Paris, France
- Calculus of Variation, Optimal transportation and Geometric Measure Theory - June 27 to July 15, 2016 Lyon, France
Network-wide training activities:
- Harmonic Analysis Program - February 1, 2017 Berkeley, United States
- Harmonic Analysis and Geometric Measure Theory - October 2, 2017 Marseille, France
- A mathematical tribute to Ennio De Giorgi - September 19-23, 2016 Pisa, Italy
- Harmonic Analysis Program - January 17 to May 26, 2017 Berkeley, United States
Outreach:
- Marie Curie Ambassador Analyse Mathématique - A.A 2014/15 Paris, France
- Marie Curie Ambassador Calculus - 2017-2018 fall PSUD, Paris, France
- Marie Curie Ambassador Analysis I - 2017-2018 spring PSUD, Paris, France
- Marie Curie Ambassador LInear Algebra - 2017-2018 spring PSUD, Paris, France
- Marie Curie Ambassador Complements of Analysis - 2017-2018 spring PSUD, Paris, France
- Workshop Day Fête de la science à l'Université Paris-Sud - October 7-11, 2015 Paris, France
- Workshop Day Journée de rentrée - A.A 2014/15 Paris, France
Talks and Poster Presentations:
- Talk: Sliding boundary cones at Sub-Riemannian Geometry Harmonic Analysis, PDE and Applications - January 24-27, 2018 Bologna, Italy
- Talk: Cones Minimaux et Calibrations at Séminaire Périodique d'analyse harmonique d'Orsay - A.A 2014/15 Paris, France
- Talk: Minimal boundary cones at MAnET MEtric Analysis Meeting - January 18-19, 2017 Paris, France
- Talk: Minimal Cones and Calibrations at Mid-term Review Meeting - December 9, 2015 Helsinki, Finland
- 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: Minimal Cones and Calibrations at Séminaire doctorant en 2° année - March 17, 2016 Paris, France
Secondment:
- UAB - June 6 to September 30, 2017 Barcelona, Spain
Publications and Preprints
- E. Cavallotto Minimal boundary cones report
- E. Cavallotto Minimal cones and calibrations report
- E. Cavallotto Sliding boundary cones report
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