Broadly speaking, I am interested in the analysis of the regularity properties and the structure of the singularities of solutions to variational problems with an underlying geometric or physical relevance, following an approach which tries to combine state-of-the-art techniques in Calculus of Variations, PDE, and Geometric Measure Theory. Topics that fascinate me, and on which I have worked (or am working) include:

• minimal surfaces;
• harmonic maps;
• branched optimal transport;
• geometric flows.

All my research is available for consultation and download on the arXiv and CVGMT portals

Publications and Preprints

1. Dynamical instability of minimal surfaces at flat singular points, with Y. Tonegawa; submitted
2. Smoothness of collapsed regions in a capillarity model for soap films, with D. King and F. Maggi; submitted
3. Collapsing and the convex hull property in a soap film capillarity model, with D. King and F. Maggi; submitted
4. An existence theorem for Brakke flow with fixed boundary conditions, with Y. Tonegawa; submitted
5. Regularity of area minimizing currents mod $p$, with C. De Lellis, J. Hirsch, and A. Marchese; to appear on Geom. Funct. Anal.  
6. Area minimizing currents mod $2Q$: linear regularity theory, with C. De Lellis, J. Hirsch, and A. Marchese; to appear on Comm. Pure Appl. Math.
7. Plateau's problem as a singular limit of capillarity problems, with D. King and F. Maggi; to appear on Comm. Pure Appl. Math.
8. A multi-material transport problem with arbitrary marginals, with A. Marchese, A. Massaccesi, and R. Tione; submitted
9. Soap films with gravity and almost-minimal surfaces, with F. Maggi and A. Scardicchio; Discrete Cont. Dyn. Syst. 39(12) (2019), 6877-6912
10. Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps, with J. Hirsch and D. Valtorta; Trans. Amer. Math. Soc. 371 (2019), no. 6, 4303-4352
11. On the lower semicontinuous envelope of functionals defined on polyhedral chains, with M. Colombo, A. De Rosa, and A. Marchese; Nonlinear Anal. 163 (2017), 201–215
12. Multiple valued sections of vector bundles: the reparametrization theorem for Q-valued functions revisited; to appear on Comm. Anal. Geom. 
13. Multiple valued Jacobi fields, Calc. Var. Partial Differential Equations 58 (2019), no. 3, Art. 92, 83 pp 
    
14. On the structure of flat chains modulo p, with A. Marchese; Adv. Calc. Var. 11 (2018), no. 3, 309–323

• Simons Travel Grant 2020 (2 yrs, 5000 USD)

In Fall 2020 I am teaching M408K - Differential Calculus (Unique Numbers 53295 and 53300).

Webpage on Canvas.

Previous Teaching:

Fall 2019: Instructor for M393C - Geometric Harmonic Maps, The University of Texas at Austin, Graduate School in Mathematics

Fall 2019: Instructor for M341 - Linear Algebra & Matrix Theory, The University of Texas at Austin

Spring 2019: Instructor for M346 - Applied Linear Algebra, The University of Texas at Austin

Fall 2018: Instructor for M361 - Theory of Functions of a Complex Variable, The University of Texas at Austin

Spring 2017: T.A. for Analysis II, University of Zurich

Fall 2016: T.A. for Mathematical Statistics, University of Zurich

Spring 2016: T.A. for Introduction to Probability, University of Zurich

Fall 2015: T.A. for Mathematics for Chemistry I, University of Zurich

Spring 2015: T.A. for Introduction to Probability, University of Zurich

Fall 2014: T.A. for ODEs and Dynamical Systems, University of Zurich

Spring 2014: T.A. for Analysis II, University of Zurich

Fall 2013: T.A. for Geometry and Topology I, University of Zurich