Publicaciones (publications)

Publicaciones de los Profesores Investigadores del Departamento de Matemática y Estadística.

Libros

Calculus off the Beaten Path: A Journey Through Its Fundamental Ideas.
Author: Ignacio Zalduendo. Springer Undergraduate Mathematics Series, 1st. edition, (2022).
This textbook provides a gentle overview of fundamental concepts related to one-variable calculus. The original approach is a result of the author’s forty years of experience in teaching the subject at universities around the world. In this book, Dr. Zalduendo makes use of the history of mathematics and a friendly, conversational approach to attract the attention of the student, emphasizing what is more conceptually relevant and putting key notions in a historical perspective. Such an approach was conceived to help them to overcome potential difficulties in teaching and learning of this subject ― caused, in many cases, by an excess of technicalities and computations.
Besides covering the core of the discipline ― real number, sequences and series, functions, derivatives, integrals, convexity and inequalities ― the book is enriched by “side trips” to relevant subjects not usually seen in traditional calculus textbooks, touching on topics like curvature, the isoperimetric inequality, Riemann’s rearrangement theorem, Snell’s law, Buffon’s needle problem, Gregory’s series, random walk and the Gauss curve, and more. An insightful collection of exercises and applications completes this book, making it ideal as a supplementary textbook for a calculus course or the main textbook for an honors course on the subject.


Game Theory and Partial Differential Equations.
Authors: Pablo Blanc and Julio Rossi. De Gruyter Series in Nonlinear Analysis and Applications, vol. 31, (2019).

Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion.

  • The first book on the subject of game theory and partial differential equations
  • Written by one of the main experts in the area
  • Of interest to researchers and graduate students in partial differential equations and applications


 Matemática para Iñaki.
Author: Ignacio Zalduendo. Fondo de Cultura Económica, México, (2017).
Quien abra este libro quizá no creerá que se trata de uno de divulgación: verá que hay ejercicios y problemas, y encontrará que todo lo que se afirma va acompañado de una demostración.
No hay duda, en cambio, de que se trata de un libro que invita al lector a adentrarse en el pensamiento matemático a través de sus conceptos más elementales, aquello que conforman la base firme de la edificación matemática: los números naturales y la aritmética; el punto y la recta; los ángulos, las funciones circulares y las ecuaciones; las permutaciones y la probabilidad.
Ignacio Zalduendo escribió este libro para Iñaki y para todo aquel que aun tiene viva su curiosidad, disfruta de los desafíos y encuentra placer en el descubrimiento que llega después de pasar un rato pensando con lápiz y papel en mano. En esto se resume, a fin de cuentas, la matemática.


Nonlocal Diffusion Problems.
Authors: Fuensanta Andreu-Vaillo, José M. Mazón, Julio Rossi and J. Julián Toledo-Melero. 
American Mathematical Society. Mathematical Surveys and Monographs. Vol. 165, (2010).
Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content.
This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the p-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin.


Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets.
Authors: José M. Mazón, Julio Rossi and J. Julián Toledo. Birkhauser. Frontiers in Mathematics, (2019).
This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them. 
These notions of nonlocal perimeter and curvature are defined on the basis of a non-singular kernel. Further, when the kernel is appropriately rescaled, they converge toward the classical perimeter and curvature as the rescaling parameter tends to zero. In this way, the usual notions can be recovered by using the nonlocal ones. In addition, nonlocal heat content is studied and an asymptotic expansion is obtained. 
Given its scope, the book is intended for undergraduate and graduate students, as well as senior researchers interested in analysis and/or geometry.


Operator Space Tensor Norms
Authors: Javier Alejandro Chávez-Domínguez, Verónica Dimant and Daniel Galicer. Springer Lecture Notes in Mathematics, vol. 2379, (2025).
This book provides a comprehensive introduction to the systematic theory of tensor products and tensor norms within the framework of operator spaces. The use of tensor products has significantly advanced functional analysis and other areas of mathematics and physics, and the field of operator spaces is no exception. Building on the theory of tensor products in Banach spaces, this work adapts the definitions and results to the operator space context. This approach goes beyond a mere translation of existing results. It introduces new insights, techniques, and hypotheses to address the many challenges of the non-commutative setting, revealing several notable differences to the classical theory. This text is expected to be a valuable resource for researchers and advanced students in functional analysis, operator theory, and related fields, offering new perspectives for both the mathematics and physics communities. By presenting several open problems, it also serves as a potential source for further research, particularly for those working in operator spaces or operator algebras.

           
  Stochastic Optimization in Insurance: A Dynamic Programming Approach. 
 Authors: Pablo Azcue and Nora Muler. Springer Briefs in Quantitative Finance, Springer, (2014).
 - A concise viscosity solution approach in insurance control problems.
 - Provides existence and structure of optimal strategies.
 - Offers systematic construction of the optimal value functions.




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