
Salvatore Stuvard
Instructor
Department of Mathematics
R. H. Bing Fellowship in Mathematics No. 1stuvard@math.utexas.edu
Phone: 5124711141
Office Location
PMA 10.132
Postal Address
2515 SPEEDWAY
AUSTIN, TX 78712

 Born in Pompei (NA), Italy;
 Italian citizen;
 Speaks English (fluent), Italian (mothertongue), German (intermediate).
Academic Positions
2018  present: Bing Instructor of Mathematics @ The University of Texas at Austin
2017  2018: Postdoctoral Researcher @ The University of Texas at Austin
Education
2013  2017: Ph.D. in Mathematics, University of Zurich, Switzerland
2010  2013: M.Sc. in Mathematics, University of Naples, Italy
2007  2010: B.Sc. in Mathematics, University of Naples, Italy

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 stateoftheart 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 almostminimal 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
 Area minimizing hypersurfaces modulo p: a geometric freeboundary problem, with C. De Lellis, J. Hirsch, A. Marchese, and L. Spolaor; preprint
 Dynamical instability of minimal surfaces at flat singular points, with Y. Tonegawa; submitted (Sep. 2020)
 Smoothness of collapsed regions in a capillarity model for soap films, with D. King and F. Maggi; submitted (July 2020)
 Collapsing and the convex hull property in a soap film capillarity model, with D. King and F. Maggi; Ann. Inst. H. Poincaré Anal. Non Linéaire, published online in Feb 2021
 An existence theorem for Brakke flow with fixed boundary conditions, with Y. Tonegawa; Calc. Var. Partial Differential Equations 60 (2021), no.1, Art. 43
 Regularity of area minimizing currents mod $p$, with C. De Lellis, J. Hirsch, and A. Marchese; Geom. Funct. Anal., 30(5) (2020), 12241336
 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
 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
 A multimaterial transport problem with arbitrary marginals, with A. Marchese, A. Massaccesi, and R. Tione; Calc. Var. Partial Differential Equations 60 (2021), no.3, Art. 88
 Soap films with gravity and almostminimal surfaces, with F. Maggi and A. Scardicchio; Discrete Cont. Dyn. Syst. 39(12) (2019), 68776912
 Rectifiability of the singular set of multiplevalued energy minimizing harmonic maps, with J. Hirsch and D. Valtorta; Trans. Amer. Math. Soc. 371 (2019), no. 6, 43034352
 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
 Multiple valued sections of vector bundles: the reparametrization theorem for Qvalued functions revisited; to appear on Comm. Anal. Geom.
 Multiple valued Jacobi fields, Calc. Var. Partial Differential Equations 58 (2019), no. 3, Art. 92, 83 pp
 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)

Teaching:
Spring 2021: Instructor for M361  Theory of Functions of a Complex Variable, The University of Texas at Austin
Fall 2020: Instructor for M408K  Differential Calculus, The University of Texas at Austin
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