Pablo Castañeda
Years at ITAM
Academic Department of Mathematics
Full time professor
I enjoy applied mathematics, which leads me to research partial differential equations, particularly conservation laws, which are a subarea of nonlinear hyperbolic equations. My interest in mathematics is broad, and I enjoy exploring areas such as dynamical systems, number theory, mathematical and numerical analysis, celestial mechanics, and fluid dynamics. My main focus is on applications in fields such as physics, chemistry, and petroleum engineering. However, I follow the maxim of the great mathematician Pál Erdős: "My brain is open." I am always willing to explore new areas and applications in which my knowledge can be useful.
© Alejandro Cisneros
I like to say that I am American, because I was born in Central America and soon moved to Mexico where I learned a lot about life and death. I have spent ten years of my training living in South America, in the beautiful Cidade Maravilhosa of Rio de Janeiro, where I acquired much of my cultural and social background. Currently, I am back in North America to work at ITAM.
Academic degrees
2004 – Mathematician
Thesis: Teoremas de singularidades en relatividad general. Faculty of Science, UNAM - Mexico.
Advisor: Pablo Padilla (IIMAS, UNAM).
2006 – Master in Computational Mathematics and Modeling
Advisor: Dan Marchesin (IMPA).
2010 – Doctor in Sciences
Thesis Chemical Reactors in Porous Media. IMPA - Brasil.
Advisors: Dan Marchesin (IMPA) and Johannes Bruining (TU-Delft).
Research interests
Partial Differential Equations, Conservation Laws, Applied Mathematics, Mathematical and Numerical Analysis.
Peer-review Journal Papers
I have had the pleasure of working with great colleagues.
S. Berres and Castañeda (2023)
"Bifurcation of solutions through a contact manifold in bidisperse models". Frontiers in Applied Mathematics and Statistics. Section Dynamical Systems 9.
[DOI: OpenAccess]
Supplementary Material: "Quasi-umbilic points".
J. Tang, Castañeda, D. Marchesin, and W.R. Rossen (2022)
"Foam-oil displacements in porous media: insights from three-phase fractional-flow theory". ADIPEC, OnePetro.
[DOI]
Castañeda, D. Marchesin, and F. Furtado (2022)
"Universality of Riemann solutions in porous media". Boletín de la Sociedad Matemática Mexicana 28: 6.
J. Tang, Castañeda, D. Marchesin, and W.R. Rossen (2019)
"Three-phase fractional-flow theory of foam-oil displacement in porous media with multiple steady states". Water Resources Research 55: 10319–10339.
Castañeda (2018)
"Explicit construction of effective flux functions for Riemann solutions", Springer Proceedings in Mathematics and Statistics 236: 273–284.
[DOI] [ResearchGate]
Castañeda, E. Abreu, F. Furtado, and D. Marchesin (2016)
"On a universal structure for immiscible three-phase flow in virgin reservoirs", Computational Geosciences 20: 171–185.
[DOI] [ResearchGate]
Castañeda and F. Furtado (2016)
"The role of sonic shocks between two- and three-phase states in porous media", Bulletin of the Brazilian Mathematical Society, New Series 47: 227–240.
[DOI] [ResearchGate]
S. Berres and Castañeda (2016)
"Identification of shock profile solutions for bidisperse suspensions", Bulletin of the Brazilian Mathematical Society, New Series 47: 105–115.
[DOI] [ResearchGate]
B. Fiedler and Castañeda (2012)
"Rainbow meanders and Cartesian billiards", São Paulo Journal of Mathematical Sciences 6: 247–275.
Castañeda, D. Marchesin, and J. Bruining (2012)
"The dynamics of chemical reactors in porous media", Advances in Differential Equations 17: 725–746.
Book chapters and preprints
Several niches where we can dialogue.
M. Núñez López, R. Zepeda-Tello, Castañeda, S. Skolnik, R. Meza, and M. Hernández-Avila (2023)
"Implementation of mitigation measures and modeling of in-hospital dynamics depending on the COVID-19 infection status", Mathematical Modelling, Simulations, and AI for Emergent Pandemic Diseases: 175–198.
[DOI]
Castañeda (2015)
"A new computational method for locating the secondary bifurcation of a Rankine-Hugoniot curve", 30º Colóquio Brasileiro de Matemática: IMPA, Rio de Janeiro, Brasil.
S. Berres and Castañeda (2015)
"Contact manifolds in a hyperbolic system of two nonlinear conservation laws", arXiv 1501.06019: 35pp.
[arXiv]
Castañeda, F. Furtado, and D. Marchesin (2015)
"Characteristic shocks for flow in porous media". IMPA preprints E41, 9pp.
Castañeda, D. Marchesin, and F. Furtado (2014)
"On singular points for convex permeability models", en Hyperbolic Problems: Theory, Numerics, Applications, HYP2012, AIMS on Applied Mathematics 8: 415–422.
V. Matos, Castañeda, and D. Marchesin (2014)
"Classification of the umbilic point in immiscible three-phase flow in porous media", en Hyperbolic Problems: Theory, Numerics, Applications, HYP2012, AIMS on Applied Mathematics 8: 791–799.
Castañeda, F. Furtado, and D. Marchesin (2013)
"The convex permeability three-phase flow in reservoirs", IMPA preprints E34, 34pp.
Castañeda, D. Marchesin, and J. Bruining (2009)
"Simulation of spontaneous ignition in porous media", Anales del Congreso Ibero-Latino-Americano de Métodos Computacionales en Ingeniería, Armação de Búzios. 30॰ CILAMCE.
Outreach essays
In science, art is to spread.
the weapon that is both most readily available
and most deadly is disclosure."
‒ Milan Kundera
R. Kaufman y Castañeda (2025)
"Any positive number is a factor of a number that descends to 1 in the ωx + 1 problem, for odd ω", The College Mathematics Journal 56: 200–202.
[DOI]
C. Bosch y Castañeda (2025)
"El billar a tres hojas", Miscelánea Matemática 80: 115–131.
[DOI] [Direct download]
V. Breña Medina, Castañeda, L. Fernández y M. Madriz Mendoza (2025)
"Alebrije matemático", Miscelánea Matemática 80: 47–65.
[DOI] [Direct download]
Castañeda (2022)
"Un determinante extraño, un breve aporte", Laberintos e Infinitos 55: 43–47.
Castañeda (2020)
"Un paso hacia los agujeros negros, generalización del colapso esférico", Motivos Matemáticos 3(1): 18pp.
Castañeda and J. Martínez Villarroya (2017)
"Las Matemáticas del mal", Laberintos e Infinitos 44: 51–62.
Castañeda (2016)
"Oleĭnik a través del espejo", Miscelánea Matemática 62: 61–80.
Castañeda (2016)
"Dogma: S-shaped. Ode to Ônibus 409", The Mathematical Intelligencer 38: 10–13.
[DOI] [ResearchGate]
Castañeda (2014)
"Primos distantes y parientes relativos", Miscelánea Matemática 58: 67–76
Castañeda y Obal (2001)
La leyenda del califa. Una travesía por los métodos de multiplicación. Folleto para el proyecto Posprimaria de CONAFE.
Sabbatical 2025
From January to December I will enjoy a sabbatical stay at the Institute of Mathematics of Ciudad Universitaria, UNAM, México. This year I will visit Antonio Capella as well as make some short stays abroad.
"The most useful science is that
whose fruit is the most communicable"
‒ Leonardo Da Vinci
Past semesters:
Linear Algebra, Differential and Integral Calculus I, Differential and Integral Calculus II, Numerical Calculus (Mathematics), Numerical Calculus Æ (Actuary and Economics), Partial Differential Equations (according to the semester with focus on Analysis, Fluid Mechanics or Numerical Methods), Analytic Geometry, Computational Mathematics, Dynamical Systems I, Dynamical Systems II.
Course notes and tutorials (Spanish)
- Notas de Matemática Computacional y Cálculo Numérico Æ (Actuarı́a y Economı́a).
- Tutorial: Breve introducción a Matlab
(In collaboration with Jimena Rodríguez Lebrija and Rodrigo Zepeda Tello). - Tutorial: Breve introducción a Python (ZIP).
Here the ReadMe. - Guide: Example of how to write mathematics with a LaTeX project [Overleaf].
Essays for course notes (Spanish)
- Convergence analysis for multi-step numerical methods.
- Classification of 2nd order PDEs.
- Generalization of the Fundamental Theorem of Calculus.
- Terse introduction to Fourier Series.
- Terse introduction to Fourier Transform.
- Terse introduction to Laplace Transform, Schaum's version.
- Notation: Big-O y small-o.
- PDE Duhamel's principle.
- ODE Existence and uniqueness theorems.
Some additional documents
- From August 2017 to December 2024 I had the privilege of coordinating the Mathematics Colloquium of the Department of Mathematics at ITAM. The person who directs it thus releases the social service, making great contributions with the organization of talks and with the beautiful posters that can be seen in this Memoirs Book.
- On March 5, 2024, I was invited by Javier Martínez Villarroya to participate in his podcast in Spanish Una Palabra, where we had the opportunity to talk about Game.
- During four semesters, from August 2014 to May 2016, I had the pleasure of directing the Mathematics Seminar of the Mathematics Department at ITAM. Here is the Book of Memories.
- This is the guide to finding the Secondary Bifurcation using an algorithm based on algebraic curves instead of nonlinear partial differential equation systems of the hyperbolic type.
Supervised theses
Armando Miguel Trejo Marrufo (2020)
"Estudio de la ecuación de Schrödinger en espacios funcionales", Bachelor's degree, ITAM; Applied mathematics.
Dalia Camacho García Formentí (2017)
"Simulación de cadenas de Markov a partir de mapeos iterativos caóticos", Bachelor's degree (special mention), ITAM; Applied mathematics.
Rodrigo Zepeda Tello (2016)
"El misterioso caso de los modelos por compartimentos: procesos de Markov, ecuaciones maestras y un programa para su estimación", Bachelor's degree (special mention), ITAM; Applied mathematics.
Theses under supervision
Daniel Tiburcio Martínez, "Criptografía con matrices de Hill rectangulares", Bachelor's degree, ITAM; Applied mathematics.
Isabel Junquera Badilla, "Model proposal for ovarian carcinoma growth and metastasis into the peritoneal cavity", Bachelor's degree, ITAM; Applied mathematics.
Francisco Gonzáles Isás, "Teorı́a y práctica en simulación de fluidos para gráficas por computadora", Bachelor's degree, ITAM; Applied mathematics.
Luis Martínez Valdés, "Soluciones al problema de Riemann en el modelo cuádratico de Corey", Bachelor's degree, ITAM; Applied mathematics.
Karen Delgado Curiel, "Aplicaciones de finanzas cuantitativas: el método de Crank-Nicolson en la valuación de opciones de barrera.", Bachelor's degree, ITAM; Applied mathematics.
Lourdes Larrea Mieres, "Classification of nature-based optimisation algorithms", Bachelor's degree, joint thesis ITAM and Essex University.
Places in the World
Delft University of Technology
Civil Engineering and Geosciences, TU-Delft – The Netherlands.
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas
Matemáticas y Mecánica IIMAS, UNAM – Mexico.
Insituto de Matemática Pura e Aplicada
Laboratório dos Fluidos, IMPA – Brazil.
Insituto Tecnoloógico Autónomo de México
Departamento de Matemáticas, ITAM – Mexico.
Universidad Nacional Autónoma de México
Facultad de Ciencias, UNAM – Mexico.
Universidade Federal de Juiz de Fora
LAMAP, UFJF – Brazil.
Sociedad Matemática Mexicana
Sociedade Brasileira de Matemática
Colleagues, interesting people
Juan Galvis
Pedro Hernández Rizzo
Bernold Fiedler
Stefan Berres
Vítor Matos
Jinyu Tang
Abdellah Salhi
Eva-Maria Graefe
© Alejandro Cisneros
