Andrea Marchese
Education 



Academic career and teaching activities 

Academic Positions
Teaching


Research interests 



Research work 

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. 

Awards and honours 



Conferences and lectures 

(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. 

Other work 

Adv. Calc. Var., 