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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
About me
Diego Alberto Barceló Nieves
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Posts
My Manim Post-Production Workflow and Tips
Published:
I have recently finished publishing a series of animated Linear Algebra videos on inner product spaces, which were created with the animation tool Manim and in collaboration with Animathica throughout three whole years. For each video, I wrote a script, directed a team of undergraduate students from UNAM’s Faculty of Sciences as they began to animate each scene, polished both the script and animations into their final form, recorded the script narration and background music, and edited everything together. I now want to write down some of what I’ve learned.
Thesis Writing Advice (Before I Forget…)
Published:
I recently finished writing a somewhat long Master’s thesis (~200 pages) in a fairly decent amount of time (about 13 months passed in between the day my advisor shared the two main articles it was to be based on -which appear cited as [Büh10] and [NP19]- with me and the day it was officially registered after being approved by a jury of 5 -without including my advisor), and learned a ton while doing so. Since many of my friends are currently in the process of writing a Master’s or undergraduate thesis, I wanted to write down some advice that can hopefully be of use to them and to others (including future me!), starting with advice given to me by others and then moving on to my own learnings.
portfolio
Inner Product, Orthogonal Bases and Vector Projections
Video which introduces the inner product as an operation that allows us to solve the problem of "finding coefficients" in finite-dimensional vector spaces in a simple and scalable manner through the use of orthogonal bases, and then uses this result to give a geometric interpretation of the inner product.
Induced Norm and Orthonormal Bases
Video which introduces the notion of norm and its relationship with inner products, as well as that of orthonormal bases, which simplify the solution to the problem of "finding coefficients" even further. (Currently in production in collaboration with Animathica; the video script and animation code can be found in this repository.)
Orthogonalization and Orthonormalization (Gram-Schmidt Theorem)
Video which illustrates the orthogonalization and orthonormalization processes in finite dimensional inner product spaces and explains the Gram-Schmidt Theorem.
publications
Una introducción a las categorías extrianguladas
Published in Universidad Nacional Autónoma de México, 2022
Recommended citation: D. A. Barceló Nieves. "Una introducción a las categorías extrianguladas". Universidad Nacional Autónoma de México, October 2022. http://132.248.9.195/ptd2022/septiembre/0831398/Index.html
talks
Telegram como herramienta de educación a distancia
Published:
Near the beginning of the SARS-CoV-2 global pandemic -which forced teaching personnel from all around the world to rapidly adapt to teaching at a distance- I gave a short workshop on how to use the Telegram Messenger app as a powerful and versatile tool for online teaching to educators of the National Autonomous University of Mexico’s Faculty of Sciences. A recording of the workshop (which was given in Spanish) can be found here.
t-Structures and (co)silting complexes
Published:
Gave the second lecture in a series of lectures by Jan Stovicek on (co)silting modules and torsion pairs at the Winter School on Large Modules and Endofiniteness. The slides and notes of said lecture can be found at the bottom of this page.
Una introducción a las categorías extrianguladas
Published:
The summary of this talk (in Spanish) may be consulted here.
Una introducción a las categorías extrianguladas
Published:
In this talk, I shared the work done for my Master’s thesis Una introducción a las categorías extrianguladas (An Introduction to Extriangulated Categories, in English) with researchers and students from Uruguay, Chile, Venezuela, Switzerland and Mexico. The presentation may be consulted here; the presentation draft in pdf format may be downloaded here. The summary is the same as the one found (in Spanish) here. A recording of the talk is available here.
Partial orderings in module degenerations
Published:
In this talk, I presented and explained the relationships between three partial orders arising from module degenerations—namely, the “deg-order”, “ext-order” and “hom-order”—as part of a Seminar on Geometrical Methods in the Representation Theory of Algebras.
On (Co)silting Bijections Involving the Category of Large Projective Presentations
Published:
The abstract of this talk may be consulted here.
On (Co)silting Bijections Involving the Category of Large Projective Presentations
Published:
The abstract of this talk may be consulted here.
teaching
Linear Algebra
Undergraduate course, National Autonomous University of Mexico, Faculty of Sciences, 2020
I taught several Linear Algebra courses, the first one -which started on January 27th, 2020- being initially in person and the rest being fully online, up until the end of 2021. The course notes and exams (in Spanish) are available in this repository. In addition to my teaching activities, I also lead a team of undergraduate students with whom I created educational Linear Algebra videos for the student-lead animation project Animathica, working as creative director, writer, animator, narrator and editor. All of our video scripts (in Spanish) and animation code may be found in this repository.
Computational Algorithms
Undergraduate course, National Autonomous University of Mexico, Faculty of Sciences, 2022
I taught a Computational Algorithms course (online) during the Spring semester of 2022, and will be doing so again in 2023. Course materials such as the syllabus, interactive notebooks, and project assignments are available (in Spanish) in this repository, whereas lecture recordings may be found here.
Modern Algebra I
Undergraduate course, National Autonomous University of Mexico, Faculty of Sciences, 2023
I taught an on-site course on Group Theory. Course notes (in Spanish) will be made publicly available via this link once they are ready.