Paolo Piovano
Tenure-Track Assistant Professor
Office: 05.136
Phone: +43 1 4277 50657
Personal eFax: +43 1 4277 850657

Wolfgang Pauli Institute (c/o University of Vienna)
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 became Universitätsassistent in his research group on Applied Mathematics and Modeling at the Faculty of Mathematics of the University of Vienna, Austria. In September 2017 following the award of some research grants as PI, I became Group Leader of the research group on Variational Methods and Applications in the same faculty. In November 2019 I completed my Habilitation (Venia Docendi) at the University of Vienna and in June 2020 I obtained the Italian national habilitation, namely the “abilitazione scientifica nazionale a professore seconda fascia - sett. conc. 01/ A3”. From November 2020 till April 2021 I had also been Visiting Professor and Excellence Chair at the Okinawa Institute of Science and Technology (OIST) in Japan. In January 2021 I was nominated Secretary and Treasurer of the The International Society for the Interaction of Mechanics and Mathematics (ISIMM). Since May 2021 I am Tenure-Track Assistant Professor (Ricercatore TD-B ``Senior’’) at the Department of Mathematics of the Polytechnic University of Milan. Concomitantly I was granted the status of Senior Research fellow at the University of Vienna and since July 2021 I am also external collaborator at the Wolfgang Pauli Institute in Vienna. http://irenefonseca.weebly.comhttp://giovannileoni.weebly.com
Research Interests
My research area is mathematical modeling, PDEs, and the calculus of variations, and my research program involves the investigation of continuum and molecular mechanics models that find applications in materials science and more recently in medical sciences. 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, the minimizing-movement method, the discrete-to-continuum passage.
Research Group (Link)
Head of the research group Variational Methods and Applications with members:
- Dr. Francesco Sapio (postdoc, from October 1, 2021);
Mr. Randy Llerena, MSc (PhD student in co-supervision with J.-F. Babadjian, U. Paris Sud, France, from September 26, 2019);
Dr. Shokhrukh Kholmatov (postdoc, from October 1, 2017);
Dr. Leonard Kreutz (postdoc, from September 18, 2017- September 17, 2018);
Mr. Filipp Lausch (Bachelor thesis with dissertation in January 2016).
Research Projects
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 (period 07.2021-07.2023, affiliated at   Wolfgang Pauli Institute, budget: ~143K Euro).
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: 01.2020-12.2022, budget: ~8K Euro).
Principal Investigator for the project with title Optimal Shapes of Crystal Interfaces granted by the Austrian Science Fund (FWF) among the Stand-Alone Projects (period: 09.2017-08.2022, from 05.2021 affiliated at the Research Platform MMM Mathematics-Magnetism-Materials with Co-Pi Prof. Norbert Mauser, project website:, budget: ~332K Euro).
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...'' (partially funded by Berndorf Foundation and the City of Vienna) and with Co-PI Prof. Ulrike Diebold, TU Vienna (period: 07.2017-04.2021, project website:, budget: ~600K Euro). 
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: 01.2019-03.2021, budget: ~156K Euro).
Short CV
External Collaborator
Polytechnic University of Milan
Department of Mathematics
P.zza Leonardo da Vinci 32, 
20133 Milano, Italy
Office: 308 (Edificio 14)
Phone: +39 02 2399 4553 
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., 53-1 (2021), 453-490, see preprint. 

16. E. Davoli, M. Kruzic, P. Piovano, U. Stefanelli, Magnetoelastic thin films at large strains, Continuum Mech. Thermodyn., 33 (2021), 327-341, 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.
Taught Courses
Polytechnic University of Milan: Lecturer at the Bachelor programs of Civil Engineering for Analysis 1 (Fall 2021) and of Engineering of Computing Systems for Analysis 2 (Fall 2021).
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). 
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).
Recent and Upcoming Presentations
August 30 - September 3, 2021, SIMAI 2020, Italian Society of Applied and Industrial Mathematics, Parma. 
May 17 - 28, 2021, SIAM MS20 (for MS33 and MS71), Bilbao, Spain (online).
November 19, 2019, Workshop RAM3, Rome, Italy. 
February 22, 2019, GAMM Annual Meeting (S14 - Applied Analysis) Vienna, Austria. 
November 12, 2018, Necas Seminar on Continuum Mechanics, Charles University, Prague, Czech Republic.  
October 28 - November 3, 2018, Oberwolfach Workshop, MFO, Germany.
September 17 - 20, 2018, joint PTM-SIMAI-UMI Mathematical Meeting, Wroclaw, Poland.
July 5 - 9, 2018, 12th AIMS Conference, Special Sessions SS75 and SS144, Taipei, Taiwan.
June 28-29, 2018, Applied Analysis Day, Dresden, Germany.
May 20 - 25, 2018, BIRS Workshop, Banff, Alberta, Canada. 
February 16, 2018, 28th Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, Italy.
Recent and Upcoming Organized Events
February 21 - 25, 2022, ESI Workshop with title Free Boundary Problems and related Evolution Equations organized together with G. Bellettini and Sh. Kholmatov at the Erwin Schrödinger International Institute for Mathematical  Physics (ESI), Vienna (postponement of the FWF event originally organized for 2020 at the University of Vienna).   
May 18 - 22, 2020, Minisymposium MS14 organized together with Profs. Francesco Solombrino and Bianca Stroffolini (U. Napoli) at SIAM MS20 in Bilbao, Spain (conference postponed).
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.