Priv-Doz Paolo Piovano

Group Leader & Senior Postdoc

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 ModelingSince September 2017 I am Project Leader & Senior Research Scientist in the same department. Since November 2019 I am Privatdozent, as I completed my habilitation at the University of Vienna. In June 2020 I obtained the Italian national habilitation, namely the “abilitazione scientifica nazionale a professore seconda fascia - sett. conc. 01/ A3”.

Research Interests

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. 

19. P. Piovano, I Velcic, Microscopical justification of solid-state wetting and dewetting, submitted (2020), see preprint.

18. Sh. Kholmatov, P. Piovano, Existence of minimizers for the SDRI model, submitted (2020), see preprint.

17. L. Kreutz, P. Piovano, Microscopic validation of a variational model of epitaxially strained crystalline films, SIAM J. Math. Anal., in press (2020), see preprint.

16. E. Davoli, M. Kruzic, P. Piovano, U. Stefanelli, Magnetoelastic thin films at large strains, Continuum Mech. Thermodyn., in press (2020), see preprint.

15. Sh. Kholmatov, P. Piovano, A unified model for stress-driven rearrangement instabilities, Arch. Ration. Mech. Anal., 238 (2020), 415-488, see preprint.

14. M. Friedrich, E. Mainini, and P. Piovano, Atomistic potentials and the Cauchy-Born rule for carbon nanotubes: a review, Rend. Semin. Mat. Univ. Politec. Torino, 77-2 (2020), 77-98, see preprint.

13. E. Davoli, P. Piovano, Derivation of a heteroepitaxial thin-film model, Interface Free Bound., 22-1 (2020), 1-26, see preprint.

12. E. Davoli, P. Piovano, Analytical validation of the Young-Dupré law for epitaxially-strained thin films, Math. Models Methods Appl. Sci., 29-12 (2019), 2183-2223, see preprint.

11. E. Mainini, P. Piovano, B.Schmidt, and U. Stefanelli, N^3/4 law in the cubic lattice, J. Stat. Phys., 179-6 (2019), 1448-1499, 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, see preprint.

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, see  repository.


Research Group (Link)

Head of the research group on Variational Methods and Applications with members (current opening available!):

  1. -Mr. Randy Llerena, MSc (PhD student in co-supervision with J.-F. Babadjian, U. Paris Sud, France, from September 26th, 2019);

  2. -Dr. Shokhrukh Kholmatov (postdoc, from October 1, 2017);

  3. -Dr. Leonard Kreutz (postdoc, from September 18, 2017- September 17, 2018);

  4. -Mr. Filipp Lausch (Bachelor thesis with dissertation in January 2016).

Research Projects

  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 ~600K 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:

  2. -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 ~332K Euro. Project website:

  3. -Co-author and co-applicant for the FWF Lise-Meitner Project with title Liquid and Crystalline Films: Wetting and Evolution with PI Sh. Kholmatov (period: 2019-2020, budget: ~156K Euro).

  4. -Principal Investigator for the Austrian side with I. Velcic (U. Zagreb, Croatia) for the Croatian side for the WTZ Grant    HR 08/2020 with title Variational Multiscale Models for Materials in the framework of the Scientific & Technological Cooperation Austria/Croatia (period: 2020-2021, budget: ~8K Euro).

  5. -Principal Investigator for the project with title Mathematical Modeling of BOne engineering (MAMBOing) granted by the Austrian Science Fund (FWF) in the framework of the 1000 Ideas Programme for the duration of 23 months with budget of ~143K Euro.

Short CV (Long Version)

Visiting Professor and Excellence Chair

Visiting Mathematics Professor Program

Okinawa Institute of Science and Technology (OIST)

1919-1 Tancha, Onna-son, Kunigami-gun, 

904-041919-1 Okinawa, Japan


Taught Courses

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

  2. -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).

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

  4. -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).

Recent and Upcoming Presentations

  1. -August 30 - September 3, 2021, SIMAI 2020, Italian Society of Applied and Industrial Mathematics, Parma.

  2. -May 17 - 28, 2021, SIAM MS20 (originally before postponement for MS14 and MS33), Bilbao, Spain.

  3. -November 19, 2019, Workshop RAM3, Rome, Italy.

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

  5. -November 12, 2018, Necas Seminar on Continuum Mechanics, Charles University, Prague, Czech Republic. 

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

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

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

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

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

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

Recent and Upcoming Organized Events

  1. -September 7 - 9, 2020, Workshop with title Free Boundary Problems and related Evolution Equations organized together with G. Bellettini and Sh. Kholmatov at the University of Vienna, Austria (on hold, postponement under evaluation by funding agencies).  

  2. -May 18 - 22, 2020, Minisymposium MS37 organized together with E. Davoli (U. Vienna) at SIAM MS20 in Bilbao, Spain (conference postponed).

  3. -November 11 - 15, 2019 ESI Joint Mathematics-Physics Symposium Modeling of crystalline Interfaces and Thin Film Structures, organized together with Ulrike Diebold (TU Vienna) and Irene Fonseca (CMU, Pittsburgh) at ESI, Vienna, Austria.