- Full professor, UT Austin, USA, 2016/present;
- Member, Institute for Advanced Study, Princeton, USA, January-April 2019;
- Research scientist, ICTP Trieste, Italy, 2016/2017;
- Associate professor, UT Austin, USA, 2012/2015;
- Professore associato (Associate prof.), U. Firenze, Italy, 2011/2012;
- Ricercatore (Assistant prof.), U. Firenze, Italy, 2005/2011;
- Wissenschaftlichen Assistenten C1 (Assistant prof.), U. Duisburg-Essen, Germany, 2005;
- Postdoctoral associate, MPI-MIS Leipzig, Germany, 2004;
- Ph.D. in Mathematics, U. Firenze, Italy, 2004;
- Visiting graduate student MPI-MIS Leipzig, Germany, Fall 2002 and Fall 2003;
- Visiting graduate student Carnegie Mellon University, Pittsburgh, USA, Spring 2003;
- M.S. in Mathematics, U. Firenze, Italy, 2000.
- Geometric Variational Problems for Surface Tension Driven Systems, NSF Grant DMS-2000034; 2020-current;
- FRG: New Challenges in Geometric Measure Theory, NSF Grant DMS-1854344, with Tatiana Toro and Camillo De Lellis; 2019-current;
- RTG: Analysis of Partial Differential Equations, NSF Grant DMS-1840314, as PI with Arie Israel, Natasa Pavlovic, Stefania Patrizi and Alexis Vasseur, 2019-current.
- Stability, symmetry and regularity issues in geometric variational problems, NSF Grant DMS-1265910, 2013/2016;
- FRG: Vectorial and geometric problems in the Calculus of Variations, NSF DMS-1361122, with Craig Evans, Alessio Figalli, and Ovidiu Savin; 2014/2018;
- Quantitative analysis of rigidity theorems and geometric inequalities, NSF Grant DMS-1565354, 2017/2020.
- Analysis of optimal sets and optimal constants: old questions and new results, ERC Starting Grant 258685, as coPI; PI, Aldo Pratelli; 2010/16;
- Analytic techniques for geometric and functional inequalities, ERC Advanced Grant 246923, as coPI; PI Nicola Fusco; 2009/15.
- Geometric-functional inequalities in sharp and quantitative form, GNAMPA-INdAM, from 2007.
- Salvatore Stuvard at UT Austin, since 2017;
- Matias Delgadino at ICTP Trieste, 2016-17;
- Brian Krummel at UT Austin, 2015-16.
- Ignacio Tomasetti at UT Austin, joint with L. Caffarelli, current.;
- Daniel Weser at UT Austin, current;
- Darren King at UT Austin, current;
- Cornelia Mihaila at UT Austin, graduated in 2018, then postdoctoral associate at U of Chicago;
- Robin Neumayer at UT Austin, joint with A. Figalli; graduated in 2017, then postdoctoral associate at Northwestern U.;
- Marco Caroccia at U. Pisa, joint with G. Alberti; graduated in 2015, then postdoctoral associate at Carnegie Mellon U.
- Hunter Stufflebeam (UT Austin) Allard type regularity theorems for rectifiable varifolds, Master degree thesis, 2018/19;
then graduate student at the University of Pennsylvania;
- Denis Deniz Gonzalez (ICTP Trieste) Symmetry properties of overdetermined properties with fractional laplacians, Diploma in Mathematics, 2016/17;
then graduate student at the Politecnico di Milano, Italy;
- Sumiya Basaandorj (ICTP Trieste) The existence of area minimizing graphs and minimal surfaces, Diploma in Mathematics, 2016/17;
then graduate student at Seoul National University, South Korea.
- Marco Caroccia (U. Firenze) Stime asintotiche per partizioni minimali del piano, Master degree thesis, 2011;
then graduate student at the University of Pisa, Italy.
- Berardo Ruffini (U. Firenze) Riduzione al caso radiale per una versione quantitative della disuguaglianza di Gagliardo-Nirenberg, Master degree thesis, 2010;
then graduate student at the Scuola Normale Superiore di Pisa.