Andrea Marchese
Formazione 



Carriera accademica ed attività didattica 

Academic Positions
Teaching


Interessi di ricerca 



Attività di ricerca 

My research focuses on Geometric Measure Theory and Calculus of Variations. Recently, I studied the singularities of area minimizing currents, the stability and regularity in branched transport, the structure of singular measures, and the differentiability of Lipschitz functions in metric measure spaces. 

Premi e riconoscimenti 



Convegni e conferenze 

(1) Marstrand's theorem and tangent measures. Seminario di Analisi Astratta, Università degli Studi di Milano, 6/10/2011. (2) Rademacher's theorem for Euclidean measures. Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, 9/2/2012. (3) Rademacher's theorem for Euclidean measures. Seminario di Calcolo delle Variazioni, Università di Pisa, 21/5/2012. (4) On the differentiability of Lipschitz functions. Analysis Seminar, University of Leipzig, 5/7/2012. (5) Differentiability of Lipschitz functions with respect to measures. Seminario di Analisi Astratta, Università degli Studi di Milano, 8/10/2012. (6) The Steiner tree problem revisited. Seminario di Analisi, Università degli Studi di Milano, 3/4/2013. (7) Differentiability of Lipschitz functions with respect to Radon measures. ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis, Pisa, 8/10/2013. (8) Is the restriction of Lipschitz functions an open mapping? Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, 28/1/2014. (9) Differentiability of Lipschitz functions with respect to measures. Seminario di Equazioni Differenziali e Applicazioni, Università di Padova, 27/3/2014. (10) Differentiability of Lipschitz functions with respect to measures in the Euclidean space. Seminar of PDE and Mathematical Phisics, University of Zurich, 9/10/2014. (11) Differentiability of Lipschitz functions with respect to measures in the Euclidean space. Topics in Geometric Analysis, University of Berlin, 30/10/2014. (12) Calibrations for the irrigation problem. LeipzigPrague Analysis workshop, Koenigstein, 8/5/2015. (13) Lusin type theorems for Radon measures. Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, 19/1/2016. (14) Lipschitz functions with prescribed blowups at many points. Analysis and Probability Seminar, Max Planck Institute of Leipzig, 23/2/2016. (15) Rectifiable currents with coefficients in groups and applications. Meeting in Applied Mathematics and Calculus of Variations, Roma, 16/9/2016. (16) Onerectifiable representations of Euclidean measures and applications. Geometric Measure Theory Workshop, Warwick, 10/7/2017. (17) Stability for a model of branched transportation. Geometric Analysis Seminar, Freiburg, 9/8/2017. (18) Branched transportation: stability and new models. Seminario di Calcolo delle Variazioni, Università di Pisa, 15/11/2017. (19) Branched transportation: stability and new models. Seminario su Equazioni Differenziali e Applicazioni, Università di Padova, 23/11/2017. (20) Branched transportation: stability and new models. Convegno nazionale di Calcolo delle Variazioni, Levico Terme, 15/2/2018. (21) Stability and new techniques in branched transportation. Seminario di matematica applicata, IMATI, Pavia, 13/3/2018. (22) A local minimality property of stable extremal submanifolds. Geometric Measure Theory in Verona, Verona 12/6/2018 (23) On the wellposedness of branched transportation. Calculus of Variations at ParisDiderot, Paris, 27/6/2018. (24) On the wellposedness of branched transportation. Università di Trento, 4/7/2018. (25) Local minimality of strictly stable extremal submanifolds. Università di Firenze, 19/10/2018. (26) Local minimality of strictly stable extremal submanifolds. Università di Roma La Sapienza, 12/11/2018. (27) Local minimality of strictly stable extremal submanifolds. Courant Institute of Mathematical Sciences, New York, 26/11/2018. (28) The regularity of soap bubbles. Politecnico di Milano. 21/2/2019. (29) On the geometry of soap films and soap bubbles. EPFL Lausanne. 10/5/2019. (30) The generic boundary spans a unique minimal network. Workshop on Geometric Measure Theory, Alba di Canazei (TN), 27/6/2019. (31) On the geometry of soap films and soap bubbles. Università di Trento, 1/7/2019. (32) On the geometry of soap films and soap bubbles. Università di Padova, 28/10/2019. (33) Singular Structures in the Geometry of Measures: regularity, rigidity and fine properties. Università di Trento, 6/11/2019. (34) An introduction to branched transport (short course). 2020 Focus Period for the FRG: New Challenges in Geometric Measure Theory (online), 14/9/2020. (35) Regularity of area minimizing currents modp. Geometric Measure Theory and Geometric Analysis in Moscow (online), 16/9/2020 (video). (36) On the geometry of soap films. Warwick University (online), 8/10/2020 . (37) Area minimizing currents mod p: general regularity theory. Regularity Theory for Free Boundary and Geometric Variational Problems, Levico Terme, 6/9/2021. (38) On the wellposedness of branched transportation. Optimal transport revisited, DMVÖMG Annual Conference 2021, Passau (online), 30/9/2021. (39) Optimization of Concave Energy Functionals on Networks. Bocconi University, Milan, 30/11/2021. (40) On the structure of the singular set of areaminimizing currents modulo p. University of Milan, 1/12/2021. (41) Tangent bundles for Radon measures and applications. University of California at San Diego, 10/3/2022. (42) Tangent bundles for Radon measures and applications. Convegno nazionale di Calcolo delle Variazioni, Levico Terme, 11/5/2022. (43) Geometric and analytic properties of Radon measures through their decompositions along curves. Geometric Analysis and PDE on Garda Lake, Gargnano sul Garda (BS), 810/6/2022. (44) Geometric and analytic properties of Radon measures through their decompositions along curves. Geometric Analysis and Calibrated Geometries, Zurich, 1317/6/2022. 

Altre attività 

Adv. Calc. Var., 