Rayssa Caju's homepage
About
I am currently an Assistant Professor at the Department of Mathematical Engineering at the University of Chile and Associate Research at the Center for Mathematical Modeling.
Before, I was Chair of Excellence for Young Researchers CMM-CNRS, at the Centro de Modelamiento Matemático (CNRS IRL2807), Universidad de Chile, Santiago, Chile from 2022 to 2023.
Before that I was a Post-doc at the Federal University of Paraíba and a visitor of the Geometric analysis group at the University of Chicago. I completed my P.hD at Federal University of Paraíba in 2018, under the supervision of João Marcos Bezerra do Ó and cosupervision of Fernando Codá Marques. I was also Visiting Student Research Collaborator in 2017-2018 at Princeton University under the supervision of Fernando Codá Marques.
My main interests are in Geometric Analysis and Partial Differential Equations, particularly in problems from conformal geometry and minimal surfaces/Allen-Cahn equation.
Research
Blow-up analysis of Large conformal metrics with prescribed Gaussian and geodesic curvatures https://arxiv.org/abs/2402.02467
with T. Cruz and A. Silva Santos.
Moduli space theory for complete, constant Q-curvature metrics on finitely punctured spheres
(https://arxiv.org/abs/2403.06511)
with J. Ratzkin and A. Silva Santos.
Constant Q-curvature metrics with Delaunay ends: The nondegenerate case. To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
with J.H. Andrade, J.M do O, J. Ratzkin and A. Silva Santos.
Singular solutions to Yamabe-type systems with prescribed asymptotics. Journal of Differential Equations, 2023.
with João Marcos do O and Almir Silva Santos
Ground states of semilinear elliptic equations with applications to the Allen-Cahn equation in the sphere. Calculus of Variations and Partial Differential Equations, 2022.
with Pedro Gaspar, Marco A.M. Guaraco, and Henrik Matthiesen
Solutions of the Allen-Cahn equation on closed manifolds in the presence of symmetry. To appear in Communications in Analysis and Geometry, 2021.
with Pedro Gaspar
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019.
with João Marcos do O and Almir Silva Santos
Events
Cibercoloquio Latinoamericano de Matematicas: A virtual colloquium in mathematics aimed at the Latinoamerican mathematical community, where renowned researchers share their knowledge and expertise in their respective fields.
Talks
Encuentro Sociedad Matemática de Chile 2022, sesión de Análisis y Ecuaciones Diferenciale, December 2022
IV Congresso Brasileiro de Jovens Pesquisadores em Matemática Pura, Aplicada e Estatística, Thematic Session, October 2022.
Celebrating Women in Mathematics, Geometry Session, May 2022.
XI Escola de Verão da Universidade Federal de Sergipe, March 2022.
Seminários em Métodos Matemáticos - Universidade Federal do Rio de Janeiro, February 2022.
Geometric Analysis Seminar, GeoTop - Copenhagen Center for Geometry & Topology, January 2022.
9th Workshop on Nonlinear Partial Differential Equations, Functional and Geometric Analysis, December 2021.
Partial Differential Equations Seminar, IIMECC - UNICAMP, November 2021.
Geometria do Nordeste Webinar, 2021
Differential Equations Seminar - Universidad de Chile, 2021
Seminar- UFRGS, 2021
Webinar de Jovens Pesquisadores em EDP e Matemática Aplicada, 2021
Obserminar University of Wurzburg, 2021 (Remotly)
Seminário de Análise UnB, 2021 (Remotly)
Webinar on Partial Differential Equations and Geometric Analysis -UFPB, 2021 (Remotly)
Seminário - UFC, 2021 (Remotly)
XIII Summer Workshop in Mathematics- UnB, 2021 (Remotly)
Webnário de Jovens Pesquisadores em Matemática Pura, Aplicada e Estatística: Um prelúdio ao IV CBJME, 2020 (Remotly)
II Escola de Geometria da UFS, 2020 (Remotly)
Seminário de Análise Geométrica UFAL, 2020 (Remotly)
Seminário de Análise - UFPB, 2020 (Remotly)
2 Encontro de Geometria Diferencial do Rio Grande do Sul - UFRGS, 2019
11th Brazilian-Italian Workshop on Nonlinear Differential Equations - RISM, Varese, 2019
Geometric Analysis Seminar - University of Chicago, 2018
Workshop for Women in Differential Equations - UFABC, 2018
Analysis Seminar- PUC, Rio de Janeiro, 2018.
VII Workshop in Nonlinear PDE's and Geometric Analysis - UFPB, João Pessoa, 2018
Contact
rayssacaju [at] gmail [dot] com or rcaju[at] dim [dot] uchile[dot] cl