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

• minimal and almost-minimal surfaces;
• geometric flows, particularly mean curvature flow;
• harmonic maps;
• branched optimal transport;
• segregated solutions to systems of PDE.

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 (Sep. 2020)
2. Smoothness of collapsed regions in a capillarity model for soap films, with D. King and F. Maggi; submitted (July 2020)
3. Collapsing and the convex hull property in a soap film capillarity model, with D. King and F. Maggi; submitted (Feb 2020)
4. An existence theorem for Brakke flow with fixed boundary conditions, with Y. Tonegawa; to appear on Calc. Var. Partial Differential Equations
5. Regularity of area minimizing currents mod $p$, with C. De Lellis, J. Hirsch, and A. Marchese; Geom. Funct. Anal., 30(5) (2020), 1224-1336
6. Area minimizing currents mod $2Q$: linear regularity theory, with C. De Lellis, J. Hirsch, and A. Marchese; Comm. Pure Appl. Math., published online in Nov 2020
7. Plateau's problem as a singular limit of capillarity problems, with D. King and F. Maggi; Comm. Pure Appl. Math., published online in Oct 2020
8. A multi-material transport problem with arbitrary marginals, with A. Marchese, A. Massaccesi, and R. Tione; submitted (Mar 2020)
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