Marco A. M. Guaraco

My name is Marco A. M. Guaraco. I am a L.E. Dickson Instructor at The University of Chicago with Prof. Andre Neves. In 2016, I obtained my PhD from IMPA (Brazil), under the guidance of Professor Fernando Coda Marques. Before that, I lived in Venezuela where I obtained a degree in Mathematics from Universidad Simon Bolivar, under the advice of Professor Lazaro Recht.

Curriculum Vitae

Click here to download a copy of my CV

Research

I work on Calculus of Variations, Geometric Analysis and PDE. More specifically, my current research focuses on Minimal Hypersurfaces, Min-max methods and the study of solutions to the Allen-Cahn equation.

Publications

Ground state of semilinear elliptic equations (Joint with R. Caju, P. Gaspar and H. Matthiesen) Preprint.
Multiplicity one and strictly stable Allen-Cahn minimal hypersurfaces (Joint with F. C. Marques and A. Neves) Preprint.
The Weyl Law for the phase transition spectrum and the density of minimal hypersurfaces (Joint with P. Gaspar) Geometric and Functional Analysis 29.2 (2019): 382-410.
The Allen-Cahn equation on closed manifolds (Joint with P. Gaspar) Calculus of Variations and Partial Differential Equations 57.4 (2018): 101
Min-max for phase transitions and the existence of embedded minimal hypersurfaces. Journal of Differential Geometry 108.1 (2018): 91-133

Minicourses and talks on video

Links to some lectures on video

Notes

Min-max for Allen-Cahn and other topics (Princeton University - Summer School 2019)
Cobordism alla Quillen (These are notes taken by Lazaro Recht of a course taught by Quillen at MIT on the 60s. Typed to LaTeX by myself. Beware of typos!)
Unique continuation for the Schrodinger Equation (M.Sc. monograph)

Photography

Click here for some pics taken by me.