About Me

My name is Alejandro and I am a mathematics PhD graduate from The University of Western Ontario. My research interest is in the area of real and functional analysis, more specifically, in topics associated with function spaces, interpolation of operators, harmonic analysis, and noncommutative measure theory. So far my research goal has been to develop a theory that will enable the powerful tools associated with monotone functions to be applied to functions on spaces with no fixed order. I currently looking for a postdoc position where I would have the opportunity to develop these tools in general spaces and investigate their connections with other areas of mathematics such as abstract harmonic analysis and partial differential equations.

Research statement Teaching statement


Research interests: Hardy inequalities, Function Spaces, Positive operators, Noncommutative measure theory, Fourier inequalities.

Contact

Alejandro Santacruz Hidalgo PhD in Mathematics asantacr@uwo.ca

Publications

Papers in refereed journals
2. Abstract Hardy inequalities: The case p=1 (2024)
Authors A. Santacruz Hidalgo
Journal Mathematical inequalities and applications, Vol 27, No 4
DOI doi.org/10.7153/mia-2024-27-64
Resources Pdf, Arxiv
1. Core decreasing functions (2024)
Authors A. Santacruz Hidalgo and G. Sinnamon
Journal Journal of Functional Analysis, Vol 287, No 4
DOI https://doi.org/10.1016/j.jfa.2024.110490.
Resources Pdf Arxiv

Non-refereed publications
1. Monotone Functions On General Measure Spaces (2024)
Type PhD Thesis
Supervisor Gord Sinnamon
Resources Link
2. Existence of weak solution to the Cauchy problem associated with the ARG traffic model (2017) (In Spanish)
Type Master Thesis (In Spanish)
Supervisor Juan Carlos Hernández Rincón
Resources Pdf

Teaching

Current Teaching
University of Western Ontario
Math 1229B: Methods of Matrix Algebra. Winter 2025.

Past teaching
King's University College
Math 1229A: Methods of Matrix Algebra. Fall 2024. Course notes.
University of Western Ontario
Calculus 1000A (First year calculus, Fall 2023)
National University of Colombia
Differential equations (2017-I)
Calculus in several variables (2016-II)
Integral calculus (2016-I)

Teaching development
Completed the Western certificate in university teaching and learning (2021-2023)
For detailed teaching philosphy, see my Teaching Dossier and teaching statement

Conference talks

The 50,60,80 Conference in Mathematics.
Karlstad, Sweden, August 20/2024
Title Monotonicity in Kernel operators and abstract Hardy inequalities.
Resources Abstract
Slides
Event information

Workshop in Analysis and Probability Seminar.
College Station, Texas, USA, July 17/2024
Title Abstract Hardy Inequalities and monotone functions.
Resources Abstract
Slides
Event information

Function Spaces XIII
Poznan, Poland, July 8/2024
Title Interpolation theory of Down spaces over general measure spaces.
Resources Abstract
Slides
Event information

Canadian mathematical society Summer meeting.
Saskatoon, Canada, June 2/2024
Title Generalized monotone functions in measure spaces.
Resources Abstract
Slides
Event information

Spring school on analysis 2023
Paseky nad Jizerou, Czech Republic, May 30/2023
Title Hardy operators and monotonicity in general spaces
Resources Abstract
Slides
Event information

Twelfth Ohio river analysis meeting
Cincinnati, United States of America, March 18/2023
Title Monotonicity in measure spaces and Hardy inequalities
Resources Abstract
Slides
Event information

Canadian mathematical society Winter meeting
Toronto, Canada, Dec 5/2022
Title Down spaces over a measure space with an ordered core
Resources Abstract
Slides
Event information

12th International confernece on nonlinear analysis, function spaces and applications
Prague, Czech Republic, May 30/2022
Title Monotonicity in ordered measure spaces
Resources Abstract
Slides
Video
Event information

Contact

Alejandro Santacruz Hidalgo PhD in Mathematics asantacr@uwo.ca