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, which included two long-term visits in the Fields Institute and Princeton University.

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).

      • Memberships:

      • Member of the AMS (American Mathematical Society) since Apr/2023.
      • Member of the SBM (Sociedade Brasileira de Matemática) since Apr/2023.

        • Academic appointments:

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

          Research visits:

          • 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.

              • Refereeing for:

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

                • Organizing committees:

                • Thematic Session on Geometric Measure Theory, at IMPA.

                  • Grants/Funding:

                  • 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, and some aspects of PDEs.
                    Currently, I am focused on regularity issues in GMT. For instance, regularity of currents/Caccioppoli sets minimizing an elliptic integrand and properties of their singular sets. Some questions concerning, specifically, the area integrand and its minimizing currents in high codimension (i.e., using Almgren-De Lellis-Spadaro's techniques) are also being part of my daily thoughts. Another direction I'm heading to is the regularity of stationary varifolds (more generally, with p-integrable generalized mean curvature) w.r.t. anisotropic integrands.
                  • R. Resende (2023). Lipschitz approximation for general almost area minimizing currents.
                    • -PDF file: Access here.
                    -Submitted.
                  • A. De Rosa and R. Resende (2023). Boundary regularity for anisotropic minimal Lipschitz graphs.
                    • -PDF file: Access here.
                    -Submitted.
                  • 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.
                    • -PDF file: Access here.
                    -Submitted.
                  • S. Nardulli and R. Resende (2022). Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity.
                    • - PDF file: Access here.
                    - Submitted.
                  • R. Resende (2022). On clusters and the multi-isoperimetric profile in Riemannian manifolds with bounded geometry.
                    • - DOI: 10.1007/s10883-022-09592-3. PDF file: Access here.
                    - 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.
                    • -DOI: 10.11606/D.45.2019.TDE-28082019-125158.
                  • R. Resende. (2017). Minimal and maximal surfaces. Bachelor's degree dissertation (In portuguese).

                    • Events, Talks, and Seminars

                  • Study Guide Writing Workshop in Harmonic Analysis., UPenn, 2023.
                  • Conferences On Smooth and Nonsmooth Geometric Analysis, Federal University of the ABC, 2023.
                    • -Title: "Lipschitz approximation for general almost minimizing currents"
                  • Rutgers Geometric Analysis Conference, Rutgers University, 2023.
                  • 37th Geometry Festival, Princeton University, 2023.
                  • PDE-Applied Math Seminar, University of Maryland (UMD), 2023.
                    • -Talk title: Regularity results for area minimizing $m$-currents in $\mathbb{R}^{m+n}$.
                  • 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.
                    • -Poster Title: "Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity"
                  • CIMPA Research school: Singularities and Applications, University of São Paulo, Campus São Carlos (USP), 2022.
                    • -Poster Title: "Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity"
                  • Point Configurations: Deformations and Rigidity, University College London (UCL), 2022.
                    • -Poster Title: "Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity"
                  • Isoperimetric Problems, University of Pisa, 2022.
                    • -Title: "On compactness and generalized existence results for clusters in Riemannian manifolds with bounded geometry"
                  • Conference Shape Optimization, related topics and applications, Roscoff Biological Center, 2022.
                    • -Poster Title: "Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity"
                  • Workshop on Submanifold Theory and Geometric Analysis, Federal University of Sao Carlos (UFSCAR), 2019.
                    • -Poster Title: "On (Λ, r)-minimizing sets"
                  • III Brazilian congress of young researches in pure and applied mathematics and statistics, Federal University of Parana, UFPR, 2018.
                    • -Poster Title: "Geometric measure theory"
                  • 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:

                    • 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.