CLE Moore Instructor

Massachusetts Institute of Technology (MIT), Office 2-239,77 Massachusetts Avenue, Cambridge

MA 02139, USA

*lspolaor* **at** *mit dot edu*

I am currently a CLE Moore Instructor at MIT. I completed my PhD studies in October 2015 at the University of Zurich under the supervision of Prof. Dr. Camillo De Lellis. After that I spent one year as a Postdoc at the Max Planck Institute for Mathematics in the sciences, under the supervision of Prof. Dr. Emanuele Spadaro. Last year I was a Visiting Lecturer and Research Scholar at Princeton University, under the supervision of Prof. Dr. Fernando Coda Marques.

My main areas of interest are Calculus of Variations, Partial Differential Equations and Geometric Analysis, with a particular focus on the study of regularity questions using methods from Geometric Measure Theory.

- L. Spolaor, B. Trey, B. Velichkov Free boundary regularity for a multiphase shape optimization problem, submitted (2018)
- M. Colombo, L. Spolaor, B. Velichkov On the asymptotic behavior of the solutions to parabolic variational inequalities, submitted (2018)
- M. Engelstein, L. Spolaor, B. Velichkov Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional, submitted (2018)
- M. Engelstein, L. Spolaor, B. Velichkov (Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents, accepted on Geom. Topol. (2018)
- M. Colombo, N. Edelen, L. Spolaor The singular set of minimal surfaces near polyhedral cones , submitted (2017)
- M. Colombo, L. Spolaor, B. Velichkov Direct epiperimetric inequalities for the thin obstacle problem and applications, submitted (2017)
- M. Colombo, L. Spolaor, B. Velichkov A logarithmic epiperimetric inequality for the obstacle problem, GAFA (2018)
- L. Spolaor, B. Velichkov An epiperimetric inequality for the regularity of some free boundary problems: the 2-dimensional case, to appear on CPAM (2018)
- M. Colombo, L. Spolaor Quantitative estimate on singularities in isoperimetric clusters, to appear in CAG (2019)
- F. Ghiraldin, L. Spolaor On the number of singular points for planar multivalued harmonic functions, Man. Math (2016)
- L. Spolaor Almgren's type regularity for Semicalibrated Currents, to appear on Adv. in Math. (2018)
- C. De Lellis, E. Spadaro, L. Spolaor Regularity theory for 2-dimensional almost minimal currents III: blowup, to appear in JDG (2018)
- C. De Lellis, E. Spadaro, L. Spolaor Regularity theory for 2-dimensional almost minimal currents II: branched center manifold, Ann. of PDEs (2017)
- C. De Lellis, E. Spadaro, L. Spolaor Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation , Transaction of AMS (2016)
- C. De Lellis, E. Spadaro, L. Spolaor Uniqueness of tangent cones for 2-dimensional almost minimizing currents , CPAM (2017)

- NSF grant DMS 1810645, '18-'21 ($157,841).
- AMS Simons travel grant, '18-'20 ($4,000).
- Oberwolfach Leibniz Fellow (OWL).
- Oberwolfach Leibniz Graduate Student (OWLG).
- Best Master student of the University of Trento, 2012, with money prize.
- PhD thesis: Regularity theory for a class of 2-dimensional almost area minimizing currents. awarded with distinction and money prize.

Currently I am not teaching.

- Colloquium at University of Wisconsin, 11/07/'18
- Colloquium at University of Minnesota, 11/15/'18
- Geometric analysis colloquium at The Fields Institute, 11/21/'18
- Analysis seminar at Brown, 12/07/'18
- Geometric Analysis seminar at Columbia, 03/08/'19
- AMS meeting Hawaii (Organizer and Speaker), 03/'19
- Oberwolfach, 07/'19
- DEA, 09/'19