Rafael Montezuma

My name is Rafael Montezuma, I am an Instructor of Mathematics at Princeton University. Previously I was a Research Associate with Prof. Andre Neves at Imperial College London, and a Visiting Scholar at The University of Chicago. I obtained my Doctorate in Mathematics at IMPA (Brazil), under the guidance of Prof. Fernando Coda Marques in 2015, and my Masters in Mathematics also at IMPA in 2011. I obtained a B.S. degree in Mathematics from Universidade Federal do Ceara (Brazil).

A copy of my CV can be found here.

Research

My primary research interests are in Differential Geometry and Geometric Analysis, with a focus on minimal surface theory and min-max methods for the area functional.

Publications

• On free boundary minimal surfaces in the Riemannian Schwarzschild manifold. arXiv (preprint)
• On the min-max width of unit volume three-spheres. (w/ Lucas Ambrozio) arXiv (submitted)
• On the two-systole of real projective spaces. (w/ Lucas Ambrozio) arXiv (accepted) Rev. Mat. Iberoam.
• A mountain pass theorem for minimal hypersurfaces with fixed boundaries. arXiv (submitted)
• Metrics of positive scalar curvature and unbounded widths. Calc. Var. Partial Differential Equations 55 (2016), no. 6, Art. 139, 15 pp. link
• Min-max minimal hypersurfaces in non-compact manifolds. J. Differential Geom. 103 (2016), no. 3, 475-519. link

Teaching

Princeton University - Course Instructor

• Spring 2019: MAT 202 - Linear Algebra with Applications (2 sessions)
• Spring 2018: MAT 201 - Multivariable Calculus
• Fall 2017: MAT 103 - Calculus I (2 sections)
• Spring 2016: MAT 201 - Multivariable Calculus
• Fall 2015: MAT 103 - Calculus I (2 sections)

Mini-courses

• Summer 2019: Minicourse “Extremal metrics for some variational geometric quantities”, Princeton University RTG program
• Summer 2016: Minicourse “Min-max theory for minimal surfaces”, School of Differential Geometry (Brazil)
• Summer 2015: Minicourse “Min-max theory for minimal surfaces”, UFAL (Brazil)
• Summer 2013/PCMI: Teaching assistant for the mini-course “Min-max theory and the Willmore Conjecture”, taught by F. Marques

IMPA (Brazil) - Teaching Assistant

• Jan-Feb 2013: Real Analysis
• Mar-Jun 2012: Riemannian Geometry
• Jan-Feb 2012: Differential Topology
• March-June 2011: Complex Analysis

Theses

• Min-max theory for non-compact manifolds and three-spheres with unbounded min-max widths Doctorate thesis and Slides
• On a theorem of M. Gromov about groups with polynomial growth (in Portuguese) Masters mini-thesis

Lecture notes

• Min-max theory of minimal surfaces. (Mini-course taught at the School of Differential Geometry - in Portuguese) link
• Min-max theory and the Willmore Conjecture. (taught by F. C. Marques at IHP) link
• Min-max minimal hypersurfaces in noncompact manifolds. (Oberwolfach report) link
• Minimal surfaces: variational theory and applications. (taught by F. C. Marques) link