About Me



Welcome to my webpage


Since September, 2023, I am a postdoctoral researcher at CMU (Carnegie Mellon University), mentored by prof. Robin Neumayer. I completed my Ph.D. at IME-USP under the supervision of prof. Stefano Nardulli and prof. Camillo De Lellis.

My research lies within the fields of Geometric Analysis and Geometric Measure Theory. I kindly invite you to click on the Menu to get more info about me, my research and activities.



Hard work will always overcome natural talent when natural talent does not work hard enough!
Theorems are corollaries of understanding.

Curriculum vitae



You can click on the button above to download a complete detailed (.pdf) version of my CV.


Some personal info:

  • I was born in January 04, 1996, in the city of São Paulo (county of Capão Redondo), Brazil.
  • I have a lovely wife and no kids yet!

    • Languages:

    • Portuguese is my native language;
    • I am fluent in English;
    • I am a struggling learner in Italian (intermediate level).

      • Academic appointments:

      • Sep/2023- : Postdoctoral Associate at Carnegie Mellon University.
        • -Mentor: Robin Neumayer.

        Research visits:

        • 2024: (1 week) Visiting Scholar, Institute for Advanced Study (IAS).
        • 2023: (5 months) Visiting Student Research Collaborator (VSRC), Princeton University.
        • 2022: (4 months) Thematic Program on Nonsmooth Riemannian and Lorentzian Geometry, The Fields Institute, University of Toronto.

          • Education:

          • Ago/2019-Jul/2023: Ph.D in Science at University of São Paulo.
            • -Advisor: Stefano Nardulli. Coadvisor: Camillo De Lellis.
          • Ago/2017-Jul/2019: Master degree in Science at the University of São Paulo.
            • -Advisor: Gláucio Terra. Coadvisor: Stefano Nardulli.
          • Jan/2014-Jul/2017: Bachelor degree in Mathematics at the University of São Paulo.
            • -Advisor: Gláucio Terra.
          • 2013: High school "E.E. Dr. Afiz Gebara" in Capão Redondo/São Paulo/Brazil.

            • Advising:

            • Co-advisor of Angélica Ponciano, Bruno Almeida, Marcos Agnoletto, and Victor Vergara, PhD student at the Federal University of ABC.

              • Mentoring:

              • Advisor of the Summer Experiences in Mathematical Sciences (SEMS) program entitled: ``One-dimensional Calculus of Variations". Also mentoring Brian Park and Eden Cen under the Summer Undergraduate Research Apprenticeship (SURA). Both programs take place at Carnegie Mellon University.

                • Refereeing for:

                • Calculus of Variations and Partial Differential Equations, Proceedings of the International Geometry Center.

                  • Organizing committees:

                  • Bridging Borders: International Geometric Analysis, at University of São Paulo.
                  • Session 3: Geometric Variational Problems in Smooth and Nonsmooth Metric Spaces, at University of Miami.
                  • Thematic Session on Geometric Measure Theory, at IMPA.

                    • Grants/Funding:

                    • Research Associate (RA): CNPq - 441922/2023-6.
                    • Research Associate (RA): FAPESP - 2021/05256-0.
                    • PhD Scholarship: CAPES - 88882.377954/2019-01.
                    • Master Scholarship: CNPq - 166204/2017-0.

                      • My Research

                      My main field of research is geometric measure theory (GMT). I am also interested in geometric analysis, calculus of variations, some aspects of regularity of PDEs and elliptic systems.
                    • S. Nardulli and R. Resende (2024). Interior regularity of area minimizing currents within a $C^{2,\alpha}$-submanifold.
                      • - Submitted.
                    • R. Resende (2023). Lipschitz approximation for general almost area minimizing currents.
                      • -Submitted.
                    • A. De Rosa and R. Resende (2023). Boundary regularity for anisotropic minimal Lipschitz graphs.
                      • - Communications in PDEs (CPDE).
                    • J. H. Andrade, J. Conrado, S. Nardulli, P. Piccione, R. Resende (2022). Multiplicity of solutions to the multiphasic Allen-Cahn-Hilliard system with a small volume constraint on closed parallelizable manifolds.
                      • - Journal of Functional Analysis (JFA).
                    • S. Nardulli and R. Resende (2022). Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity.
                      • - Submitted.
                    • R. Resende (2022). On clusters and the multi-isoperimetric profile in Riemannian manifolds with bounded geometry.
                      • - Journal of Dynamical and Control Systems (JDCS).
                    • R. Resende (2023). Some regularity results in geometric measure theory.
                      • PhD thesis.
                    • R. Resende. (2019). Regularity of almost minimizing sets. Master's degree dissertation.
                    • R. Resende. (2017). Minimal and maximal surfaces. Bachelor's degree dissertation (In portuguese).

                      • Events, Talks, and Seminars

                    • Math Seminar, Federal University of ABC, 2023.
                    • Geometric Measure Theory and applications, Palazzone SNS in Cortona, 2024.
                    • Workshop on Advising and Mentoring Graduate Students and Postdocs, Rice University, 2023.
                    • CNA Seminar, CMU, 2023.
                    • Study Guide Writing Workshop in Harmonic Analysis, UPenn, 2023.
                    • Conferences On Smooth and Nonsmooth Geometric Analysis, Federal University of the ABC, 2023.
                    • Rutgers Geometric Analysis Conference, Rutgers University, 2023.
                    • 37th Geometry Festival, Princeton University, 2023.
                    • PDE-Applied Math Seminar, University of Maryland (UMD), 2023.
                    • Recent trends in nonlinear and geometric analysis, CUNY Graduate Center, 2023.
                    • Hausdorff School on Geometric Analysis and Nonlinear Partial Differential Equations, Hausdorff Center for Mathematics (HCM), 2022.
                    • CIMPA Research school: Singularities and Applications, University of São Paulo, Campus São Carlos (USP), 2022.
                    • Point Configurations: Deformations and Rigidity, University College London (UCL), 2022.
                    • Isoperimetric Problems, University of Pisa, 2022.
                    • Conference Shape Optimization, related topics and applications, Roscoff Biological Center, 2022.
                    • Workshop on Submanifold Theory and Geometric Analysis, Federal University of Sao Carlos (UFSCAR), 2019.
                    • III Brazilian congress of young researches in pure and applied mathematics and statistics, Federal University of Parana, UFPR, 2018.
                    • Modern Trends in Differential Geometry, IME-USP, 2018.
                    • Symposium in Harmonic Analysis and Geometric Measure Theory, USP-Ribeirão Preto, 2018.

                      • Teaching



                      Teaching at Carnegie Mellon University:

                      • Fall 2024: 21-356: "Principles of Real Analysis II". See Canvas for more info.
                      • Summer 24: 21-127: "Concepts of Mathematics". See Canvas for more info.
                      • Spring 2024: 21-356: "Principles of Real Analysis II". See Canvas for more info.
                      • Fall 2023: 21-356: "Principles of Real Analysis II". See Canvas for more info.

                        • Teaching at University of São Paulo:

                        • 2023: "Introduction to linear algebra" at IME-USP.
                        • 2022: "Metric spaces" at IME-USP.

                          • Teaching Assistant:

                          • 2022: "Differential and integral calculus I" at IGc-USP, 2022.
                          • 2021: "Differential Geometry" and "Series and differentiable functions" at IME-USP.
                          • 2020: "Calculus of multivariable functions II" and "Metric spaces", Summer Course, at IME-USP. Differential and integral calculus I at IAG-USP.
                          • 2019: "Linear algebra", Summer Course, and "Analytic geometry" at IME-USP.
                          • 2018: "Linear algebra II" and "Measure and integration" at IME-USP.
                          • 2017: "Introduction to linear algebra" at IME-USP.