Andrea Marchese

• 2013: PhD in Mathematics at University of Pisa. Advisor: prof. Giovanni Alberti. PhD Thesis: "Two applications of the theory of currents".
• 2008: Master degree in Mathematics at University of Milano. Final mark: 110/110 with honor. Advisor: prof. Clemente Zanco. Thesis: "Punti singolari per coperture di spazi di Banach" (Singular points for coverings of Banach spaces).
• 2006: Bachelor degree in Mathematics at Università degli Studi di Milano. Final mark: 110/110 with honor. Advisor: prof. Clemente Zanco. Thesis: "Topologie deboli e loro metrizzabilità in spazi di Banach" (Weak topologies and their metrizability in Banach spaces).

Academic Positions

• 2019-Present: Assistant Professor (RTDb) at Mathematics Department, University of Trento.
• 2018-2019: Assistant Professor (RTDa) at Mathematics Department "F. Casorati", University of Pavia.
• 2015-2018: Postdoc at University of Zurich. Research Group lead by prof. Camillo De Lellis, supported by the ERCgrant 306247 "Regularity of area minimizing currents" and by the SNFgrant 154903 "Regularity questions in geometric measure theory".
• 2012-2015: Postdoc at Max Planck Institute Leipzig. Research Group "Geometric Measure Theory and Applications" lead by prof. Emanuele Spadaro.

Teaching

• March-June 2021 and 2022: Lectures for the course "Mathematical Analysis 2" at University of Trento for the degree course in Industrial Engineering.
• February - June 2021 and 2022: Lectures for the course "Geometric Measure Theory" at University of Trento for the master course/PhD in Mathematics (42 hours).
• February - May 2020: Lectures for the course "Geometry and Linear Algebra" at University of Trento for the degree course in Industrial Engineering.
• November 2019- January 2020: Lectures for the course "Functional Analysis" at University of Pavia for the master course in Mathematics and Physics.
• March - June 2019: Lectures for the course "Mathematical Analysis 2" at University of Pavia for the degree course in Electronic and Computer Science Engineering.
• December 2018-March 2019: Lectures for the course "An introduction to the theory of currents" at University of Pavia for the PhD in Mathematics (24 hours).
• December 2018-January 2019: Lectures for the course "Complements of Mathematical Analysis" at University of Pavia for the degree course in Civil Engineering.
• March - June 2018: Lectures for the course "Mathematical Analysis 2" at University of Pavia for the degree course in Industrial Engineering.
• October 2017 - February 2018: Lectures for the course "Geometric Measure Theory" at Albert-Ludwigs-University of Freiburg for the master course/PhD in Mathematics (24 hours).
• October - December 2017: Exercise classes for the course "Analysis II" at University of Zurich for the degree course in Mathematics and Physics.
• March - June 2017: Lectures for the course "Selected topics in Geometric Measure Theory" at University of Zurich for the master course/PhD in Mathematics (24 hours).
• September 2016 - February 2017: Lectures for the course "An introduction to Geometric Measure Theory" at University of Zurich for the master course/PhD in Mathematics (24 hours).
• March - June 2016: Exercise classes for the course "Convex Optimization" at University of Zurich for the master course in Mathematics.
• September 2015 - February 2016: Exercise classes for the course "Analysis I" at University of Zurich for the degree course in Mathematics and Physics.
• April - August 2015: PhD course "Geometry of Euclidean measures: densities and rectifiability" at Max Planck Institute Leipzig (20 hours).
• October 2013 - February 2014: Exercise classes for the PhD course "Partial differential equations III" at Max Planck Institute Leipzig.
• April - June 2013: Exercise classes for the PhD course "Introduction to rectifiable currents" at Max Planck Institute Leipzig.
• November 2011 - January 2012: Exercise classes for the course "Mathematics" at University of Pisa for the degree course in Natural environmental sciences.
• January - July 2010 and November 2010 - May 2011: Exercise classes for the course "Mathematics" at University of Pisa for the degree course in Geology.
• September - December 2008: Exercise classes for the course "Analysis I" at Politecnico of Milano for the degree course in Automatic Engineering.

1. Geometric Measure Theory
2. Calculus of Variations
3. Minimal surfaces
4. Optimal transport

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.

• from 01/06/2022: Habilitation for Full Professor in Mathematical Analysis.
• 2022-2023: participant to the project "Geometric Measure Theory and Applications", supported by "GNAMPA-INdAM" (3000 EUR)
• 2020: ERC Starting Grant (not funded), Final Score A (fully meets the Awards ERC’s excellence criterion and is recommended for funding if sufficient funds are available). Ranking: 484 out of 3272 submitted proposals (437 selected).
• from 09/09/2019: Habilitation for Associate Professor in Mathematical Analysis.
• 15/7/2019: awarded from University of Pavia of grant "INROAd-T.O.C.A." (Theory of Currents and Applications) (5.000 EUR).
• 26/04/2019: appointed from INdAM for the organization of the meeting "Geometric Measure Theory and Applications" (financial support: 15.000 EUR).
• 2019-2020: coordinator of the project "Applicazioni della Teoria delle Correnti all'Analisi Reale e al Trasporto Ottimo", supported by "GNAMPA-INdAM" (4.800 EUR).
• 2019-present: participant to PRIN "Gradient Flows, Optimal Transport and Metric Measure Structures", coordinated by Luigi Ambrosio.
• 2018-2019: participant to the project "Geometric Measure Theoretical approaches to Optimal Networks", supported by "GNAMPA-INdAM" (4.500 EUR).
• 6/3/2018: "Marie Sklodowska-Curie Actions Seal of Excellence".
• 12/2016: "Graduate Campus Grant" at University of Zurich (10.000 CHF) .
• 2016: "Qualifcation" for Maitre de Conference in Mathematics in France.
• 2013-2016: participant to PRIN "Calcolo delle Variazioni", coordinated by da Gianni Dal Maso.
• 2010-2012: participant to PRIN "Teoria del trasporto ottimo, disuguaglianze geometriche e funzionali: applicazioni all'ottimizzazione geometrica ed allo studio di fenomeni di congestione e di ramificazione", coordinated by Luigi Ambrosio.
• 2003-2006: bachelor scholarship INdAM (12.300 EUR).

(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. Leipzig-Prague 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) One-rectifiable 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 well-posedness of branched transportation. Calculus of Variations at Paris-Diderot, Paris, 27/6/2018.

(24) On the well-posedness 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), 1-4/9/2020.

(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 well-posedness of branched transportation. Optimal transport revisited, DMV-ÖMG 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 area-minimizing 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), 8-10/6/2022.

(44) Geometric and analytic properties of Radon measures through their decompositions along curves. Geometric Analysis and Calibrated Geometries, Zurich, 13-17/6/2022.

• 29-31/08/2022: organizer of summer school "Three days between analysis and geometry in Trento".
• 09-13/05/2022: local organizer of "XXXI Convegno Nazionale di Calcolo delle Variazioni", Levico Terme.
• 03/2022-06/2022: organizer of reading seminar "Optimal transport and applications", Trento.
• 11/2020-12/2020: organizer of reading seminar (online) "The De Giorgi method for elliptic equations", Trento.
• 12/2020-present: organizer of "Analysis Seminars" in Trento.
• 14-18/6/2021: organizer of "Geometric Measure Theory and applications", Cortona (IT),
• 16-17/1/2020: organizer of "Geometric Measure Theory in Padova".
• 24-28/9/2018: organizer of "Workshop MAR: Metric Analysis and Regularity" (70 participants).
• 24-26/4/2017: organizer of "Transport problems in Zurich" (50 participants).
• 2013-2015: organizer of "Arbeitsgemeinschaft Angewandte Analysis" at Max Planck Institute of Leipzig.
• Referee of more than 40 papers for more than 30 journals, including:

Adv. Calc. Var.,
Ann. Sci. Ecole Norm. Sup.,
Ann. Scuola Norm. Sup. Pisa Cl. Sci.,
Appl. Math. Optim.,
Arch. Ration. Mech. Anal.,
Bull. London Math. Soc
Calc. Var. Partial Differential Equations,
Comm. Pure Appl. Math.,
Int. Math. Res. Not.,
Invent. Math.,
J. Diff. Geom.
J. Éc. polytech. Math.
J. Eur. Math. Soc.,
J. Funct. Anal.,
J. Geom. Anal.,
J. London Math. Soc.,
Nonlinear Anal.,
Proc. London Math. Soc.,
Potential Anal.,
SIAM J. Math. Anal.