Supervisor: Prof. Matteo Novaga

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Summary of the academic activities performed during the PhD course

Marco Pozzetta

Supervisor: Prof. Matteo Novaga

Attended courses and exams

• Network Optimization Problems, Prof. Eugene Stepanov, 2017-2018 PhD course UniPi.

• Alcuni argomenti di Analisi Geometrica in spazi metrici ed in strutture non riemanniane, Prof.

Valentino Magnani, 2017-2018 PhD course UniPi.

• Initial data sets in General Relativity, Prof. Alessandro Carlotto, 2017-2018 PhD course SNS, Grade: Ottimo.

• Elliptic PDEs, Prof. Luigi Ambrosio, 2017-2018 PhD course SNS, Grade: 30.

• Geometric flows, Prof. Andrea Malchiodi, 2017-2018 PhD course SNS, Grade: 30 L.

• Optimal Transport, Prof. Luigi Ambrosio, 2018-2019 PhD course SNS.

• Variational analysis of Liouville type equations, Prof. Aleks Jevnikar, 2018-2019 PhD course UniPi.

• Variational methods, Prof. Andrea Malchiodi, 2018-2019 PhD course SNS.

• Geometria delle sottovariet` a, Prof. Luciano Mari, 2018-2019 Graduate/PhD course SNS.

Publications and preprints

• Dayrens F., Masnou S., Novaga M., Pozzetta M. : Connected perimeter of planar sets, Adv. Calc.

Var. 2020.

• Del Nin G., Pluda A., Pozzetta M., Degenerate elastic networks, J. Geom. Anal. 2020.

• Novaga M., Pozzetta M. : Connected surfaces with boundary minimizing the Willmore energy, Mathematics in Engineering, 2020, 2(3): 527-556.

• Pozzetta M. : On the Plateau-Douglas problem for the Willmore energy of surfaces with planar boundary curves, ESAIM: COCV 2020.

• Pozzetta M. : A varifold perspective on the p-elastic energy of planar sets, J. Conv. Anal. 27 (2020), No. 3, 845-879.

• Pozzetta M. : Confined Willmore energy and the Area functional, Comm. Anal. Geom. 2020.

• Mantegazza C., Pluda A., Pozzetta M. : A survey of the elastic flow of curves and networks, Preprint.

• Mantegazza C., Pozzetta M. : The Lojasiewicz–Simon inequality for the elastic flow, Preprint.

• Pozzetta M. : Convergence of elastic flows of curves into manifolds, Preprint.

Talks

• 5/6/20 - An introduction to varifold geometry and applications, Invited online talk at SISSA, Trieste, Analysis Junior Seminars - Webinar Edition.

• 4/12/19 - On the elastic energy of planar sets, Invited talk at Universit` a di Napoli Federico II.

• 29/10/19 - An introduction to varifold geometry and applications, Invited talk at Universit` a di Trento, Doc in Progress series of seminars, Trento.

• 4/2/19 - Il problema di Plateau-Douglas per l’energia di Willmore, Contributed talk at XXIX Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, Trento.

• 4/12/18 - On the Plateau-Douglas problem for the Willmore energy, Invited talk at University of Freiburg.

• 7/11/18 - On the Plateau-Douglas problem for the Willmore energy, Invited talk, permanent series of seminars in Calculus of Variations, Universit` a di Pisa.

• 6/03/18 - Minimizing the Willmore energy and related functionals with a varifold approach, Con- tributed talk at Workshop on Geometric Evolution Equations, University of Regensburg.

• 27/02/18 - Il funzionale di Willmore e il metodo diretto dell’approccio varifold, Invited talk in the

series of seminars: Seminari MAP, Universit` a di Pisa.

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Visits

• 2-6/12/19 - Visit at Universit` a di Napoli Federico II invited by Prof. Carlo Mantegazza.

• 3-7/12/18 - Visit at University of Freiburg invited by Prof. Ernst Kuwert.

Teaching

• 2019-2020 - Teaching assistant for the course “Analisi Matematica I” at the faculty of Mathematics, Universit` a di Pisa. Professor of the course: Prof. Matteo Novaga.

• 2018-2019 - Reading course “Motion of Level Sets by Mean Curvature”, Universit` a di Pisa. Course in collaboration with Valerio Pagliari.

• 2017-2018 - Teaching assistant for the course “Analisi Matematica II e Complementi” at the faculty of Chemical Engineering and Energetic Engineering, Universit` a di Pisa. Professor of the course:

Prof. Valentino Magnani.

Attended conferences and schools

• 3-7/02/20 - XXX Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, Trento.

• 25-28/11/19 - Recent trends in Geometric Analysis and applications, Centro di ricerca De Giorgi, Pisa.

• 16-19/09/19 - 6

^th

Applied Mathematics Symposium M¨ unster: recent advances in the Calculus of Variations, University of M¨ unster.

• 3-7/06/19 - Geometric Analysis and General Relativity. A conference in honour of Gerhard Huisken, ETH Zurich.

• 14-17/01/19 - Conference in honour of Alessio Figalli, Fields medallist 2018, SNS Pisa.

• 4-8/02/19 - XXIX Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, Trento.

• 16-20/07/18 - Summer School on Einstein Equations, Domodossola (VB).

• 18-22/06/18 - CIME summer school in Geometric Analysis, Cetraro (CS).

• 5-8/03/18 - Workshop on Geometric Evolution Equations, University of Regensburg.

• 12-16/02/18 - XXVIII Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, Trento.

Other activities

• June 2020 - Completed the “Percorso formativo 24 CFU”.

• 2020 - Member of the INdAM-GNAMPA Project 2020 Minimal clusters and minimal partitions, P.I. Alessandra Pluda.

• 2019-2020 - Co-organizer of Seminari MAP: Metodi per l’Analisi e la Probabilit` a in collaboration with Alessandra Pluda and Vincenzo Scattaglia.

• 2019 - Member of the INdAM-GNAMPA Project 2019 Problemi geometrici per strutture singolari, P.I. Alessandra Pluda.

• 2018-2020 - Representative of the PhD students of the Dipartimento di Matematica at Universit` a di Pisa, in collaboration with Chiara Spagnoli.

• 2018-2019 - Co-organizer of Seminari MAP: Metodi per l’Analisi e la Probabilit` a in collaboration

with Valerio Pagliari, Alessandra Pluda and Vincenzo Scattaglia.