CLE Moore Instructor

Massachusetts Institute of Technology (MIT), Office 2-241,77 Massachusetts Avenue, Cambridge

MA 02139, USA

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

I am currently a Visiting Associate Research Scholar and Visiting Lecturer at Princeton University on leave from MIT, where I am employed as a CLE Moore Instructor since September 2016. 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.

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

- 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, submitted, 2017
- L. Spolaor, B. Velichkov An epiperimetric inequality for the regularity of some free boundary problems: the 2-dimensional case, submitted, 2017
- M. Colombo, L. Spolaor Quantitative estimate on singularities in isoperimetric clusters, CAG, 2017
- 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, submitted, 2015
- C. De Lellis, E. Spadaro, L. Spolaor Regularity theory for 2-dimensional almost minimal currents III: blowup, to appear in JDG, 2017
- C. De Lellis, E. Spadaro, L. Spolaor Regularity theory for 2-dimensional almost minimal currents II: branched center manifold, to appear in Ann. of PDEs, 2017
- C. De Lellis, E. Spadaro, L. Spolaor Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation , to appear in Transaction of AMS, 2016
- C. De Lellis, E. Spadaro, L. Spolaor Uniqueness of tangent cones for 2-dimensional almost minimizing currents , to appear in Comm. Pure App. Math., 2016

- 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 teaching MAT 103 at Princeton University.