Paolo Piovano

Project Leader & Senior Research Scientist

Office: 05.136

Phone: +43 1 4277 50657
Personal eFax: +43 1 4277 850657


University of Vienna

Faculty of Mathematics

Oskar-Morgenstern-Platz 1,

1090 Wien, Austria

I received my Ph.D. in Mathematical Sciences from Carnegie Mellon University, USA in June 2012 under the supervision of Irene Fonseca and Giovanni Leoni.

After a postdoctoral position of one year under the mentorship of Prof. Ulisse Stefanelli at the National Research Council of Italy, Institute of Applied Mathematics and Information Technology (CNR-IMATI) in Pavia, Italy, I have been employed at the Faculty of Mathematics of the University of Vienna, Austria as Universitätsassistent in the research group on Applied Mathematics and Modeling. Since September 2017 I am Project Leader & Senior Research Scientist in the same department.

Research Interests

Short CV

Research Projects

  1. -Principal Investigator for the Stand-Alone Project with title Optimal Shapes of Crystal Interfaces granted by the Austrian Science Fund (FWF) for the duration of 4 years starting on September 1st, 2017 with budget of 332,262.00 Euro. Project website:

  1. -Principal Investigator for the project with title Modeling and Design of Epitaxially Strained Nanoislands awarded by the Vienna Science and Technology Fund (WWTF) in the framework of the 2016 Program ``Mathematics and...'' for the duration of 4 years starting on July 1st, 2017 with budget of 596,200.00 Euro (partially funded by Berndorf Foundation and the City of Vienna) and with Co-PI Prof. Ulrike Diebold, Institute of Applied Physics, TU Vienna. Project website:

Research Group

Head of the research group on Variational Methods and Applications

P.'s research area is PDEs and the Calculus of Variations, and his research program involves the investigation of Continuum and Molecular Mechanics models that find applications in Materials Science. The focus is on free boundary problems and atomistic models motivated by applications in the study of the epitaxial growth of thin films, the optimal shapes of crystal interfaces, and the stability of molecular structures.

The methodology includes configurational energy minimization, isoperimetric characterization, Gamma-convergence, and the minimizing-movement method (Curriculum Vitae).

Upcoming Workshop (11-15.11.2019): Modeling of crystalline Interfaces and Thin Film Structures: a Joint Mathematics-Physics Symposium, organized together with Ulrike Diebold (TU Vienna) and Irene Fonseca (CMU, Pittsburgh) at ESI, Vienna.




15. Sh. Kholmatov, P. Piovano, A unified model for stress-driven rearrangement instabilities, Submitted (2019). See preprint.

14. L. Kreutz, P. Piovano, Microscopic validation of a variational model of epitaxially strained crystalline films, Submitted (2019). See preprint

13. E. Mainini, P. Piovano, B.Schmidt, and U. Stefanelli, N^3/4 law in the cubic lattice, Submitted (2018). See preprint.

12. E. Davoli, P. Piovano, Analytical validation of the Young-Dupré law for epitaxially-strained thin films, Submitted (2018). See preprint.

11. E. Davoli, P. Piovano, Derivation of a heteroepitaxial thin-film model, Submitted (2018). See preprint.

10. M. Friedrich, E. Mainini, P. Piovano, and U. Stefanelli, Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule, Arch. Ration. Mech. Anal., 231-1 (2019), 465-517.  See preprint.

9. E. Mainini, H. Murakawa, P. Piovano, and U. Stefanelli, Carbon-Nanotube Geometry as Optimal Configurations, Multiscale Model. Simul.15-4 (2017), 1448--1471. See preprint.

8. E. Davoli, P. Piovano, and U. Stefanelli, Sharp N^{3/4} Law for the Minimizers of the Edge-Isoperimetric Problem on the Triangular Lattice, J. Nonlinear Sci., 27-2 (2017), 627--660. See preprint

7. M. Friedrich, P. Piovano, and U. Stefanelli, The Geometry of C_60: A Rigorous Approach via Molecular Mechanics, SIAM J. Appl. Math., 76-5 (2016), 2009-2029. See preprint.

6. E. Davoli, P. Piovano, and U. Stefanelli, Wulff Shape Emergence in Graphene, Math. Models Methods Appl. Sci., 26-12 (2016), 2277-2310. See preprint.

5. E. Mainini, H. Murakawa, P. Piovano, and U. Stefanelli, Carbon-nanotube Geometries: Analytical and Numerical Results, Discret. Contin. Dyn. Syst. Ser. S, 10 (2017), 141-160. See preprint.

4. E. Mainini, P. Piovano, and U. Stefanelli, Crystalline and Isoperimetric Square Configurations, Proc. Appl. Math. Mech., 14 (2014), 1045-1048. See preprint.

3. E. Mainini, P. Piovano, and U. Stefanelli, Finite Crystallization in the Square Lattice, Nonlinearity, 27 (2014), 4:717-737. See preprint.

2. P. Piovano, Evolution of Elastic Thin Films with Curvature Regularization via Minimizing Movements, Calc. Var. Partial Differential Equations, 49 (2014), 337-367. Preprint available at

1. P. Piovano, Evolution and Regularity Results for Epitaxially Strained Thin Films and Material Voids, ProQuest; Thesis (Ph.D.)-Carnegie Mellon University 2012; ISBN: 9781267655349; Vol. 74-01(E), Sect. B.; p. 108. Available at and at

Taught Courses

  1. -University of Vienna: Lecturer at the Faculty of Mathematics for the following graduate-level courses: The Direct Method in the Calculus of Variations (Fall 2019), Topics in the Calculus of Variations (Spring 2018).

  1. -University of Vienna: Teaching Assistant at the Faculty of Mathematics for the following exercises courses: Partielle Differentialgleichungen (Fall 2016), Analysis (Spring 2016), Höhere Analysis und Differentialgeometrie (Fall 2015), Analysis (Spring 2015), Einführung in das mathematische Arbeiten and Einführung in die Analysis (Fall 2014), Modellierung (Fall 2013).

- Webster University Vienna, Austria: Lecturer for the undergraduate course College Algebra (Fall 2016).

- Carnegie Mellon University, USA: Teaching Assistant at the Department of Mathematics for the following exercises courses: Calculus in Three Dimensions (Spring 2011) and Differential Equations (Fall 2010).

Supervised Students

Mr. Filipp Lausch, Bachelor thesis at the Department of Mathematics, University of Vienna with thesis dissertation on January 20, 2016.

Recent and Upcoming Presentations

  1. -February 22, 2019, GAMM Annual Meeting (S14 - Applied Analysis) Vienna, Austria.

  2. -November 12, 2019, Necas Seminar on Continuum Mechanics, Charles University, Prague, Czech Republic. 

  3. -October 28 - November 3, 2018, Oberwolfach Workshop, MFO, Germany.

  4. -September 17 - 20, 2018, joint PTM-SIMAI-UMI Mathematical Meeting, Wroclaw, Poland.

  5. -July 5 - 9, 2018, 12th AIMS Conference, Special Sessions SS75 and SS144, Taipei, Taiwan.

  6. -June 28-29, 2018, Applied Analysis Day, Dresden, Germany.

  7. -May 20 - 25, 2018, BIRS Workshop, Banff, Alberta, Canada.

  8. -February 16, 2018, 28th Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, Italy.