- When I was at the University of Michigan, I taught an introductory course to set theory (MATH 582) three times, which gave me ample opportunity to compile the material that I used to teach that class (which wasn't based on any single textbook). The result is the following set of notes , which more or less faithfully reflects my view of how the topic should be learned. I'm extremely open to (and will be very grateful for) any comments or suggestions. I hope to be able to turn these (after some further completing and polishing) into a book some day.
- One of the results of my paper (joint with Michael Hrušák) on Gruff ultrafilters had a serious mistake (discovered by Osvaldo Guzmán), which prompted us to eventually publish a corrigendum (in fact, the mistake in this paper can be traced back to an old paper of Paul E. Cohen (not to be confused with the Paul J. Cohen that discovered forcing!), thus turning the statement that there are P-points in the random model from a theorem back into an open problem). Attempts to fix that proof led me to formulating the definition of a "generalized pathway", a set-theoretic device whose existence allows to perform certain mathematical constructions in much the same way that assuming a certain a cardinal characteristic to be large does. All I know about these objects is written in this set of notes . I don't have any plans to try and publish this in the near future (there is still much work to be done before the notes are sufficiently valuable, and I'm currently mostly focused on other research projects), but some people have found them valuable, so I put them here (however, if you plan to cite these notes, it's probably more optimal to cite the arXiv version).
- A set of notes (in Spanish) on club and diamond , two well-known combinatorial principles of Set Theory. In order to understand the last section, knowledge of the forcing technique is required.
- Back in my youth, I wrote some notes on ordinal numbers (in Spanish), including an interesting discussion on the Axiom of Infinity. (I used to have plans to complement these by adding a part on cardinal numbers, but by now it's clear that this is just non going to happen.)

- Slides from my talk
*Independence proofs, what are they (good for)?*(*Pruebas de independencia: ¿Qué son y para qué sirven?*), Mathematics Seminar, ESFM-IPN. - Slides from my talk
*From integral calculus to the mysteries of infinity*, which took place on October 19^{th.}, 2021, via Zoom, but officially at Universidad Nacional Federico Villarreal, Peru. - Slides from my talk
*Ramsey Theory on Infinite Additive Structures*, which took place on September 14^{th.}, 2021, within the Combinatorics, Control and Optimization Seminar at Universidad Autónoma Metropolitana - Azcapotzalco. - Slides from my talk
*Hindmanâ€™s theorem as a weak version of the Axiom of Choice*, which took place on June 19^{th.}, within the Boise Extravaganza in Set Theory 2021 conference. - Slides from my talk
*Comparing the difficulty of combinatorial results using Mathematical Logic*, which took place on May 18^{th.}, within the conference Interacciones en la Frontera 2021. - Slides from the first talk of the minicourse on
*Ramsey Theory and Applications*, which took place on May 17^{th.}, within the conference Interacciones en la Frontera 2021. - Slides from the talk
*Ends of nonmetrizable manifolds: a generalized bagpipe theorem*, which took place on May 12^{th.}, within the Spring Topology and Dynamics Conference 2021. - Slides from the talk
*Variations on a theme: Ramsey's and Hindman's theorem*, which took place on August 9^{th.}, within the BLAST 2018 conference. - Slides from the talk
*Algebraic Ramsey-Theoretic Statements with an Uncountable Flavour*, which took place on November 14^{th.}, 2017, within the Second Pan Pacific International Conference on Topology and its Applications. - Slides from the talk
*Strong negations of Hindman's theorem for uncountable FS-sets*, which took place on October 8^{th.}, 2016, within the AMS Fall Western Sectional Meeting. - Slides from the talk
*Strong failures of higher analogs of Hindman's theorem*, which took place on September 14^{th.}, 2016, within the Workshop on Set Theory and its Applications in Topology. - Slides from the talk
*Set Theory (sometimes) can solve your problem!*, which was my "Capsule Research Talk" (an annual series of short talks, at the Department of Mathematics, University of Michigan, given by the incoming postdocs in order to introduce the Department members to their research), August 31^{st.}, 2015. - Slides from the talk
*Una Introducción Amable a la Teoría Infinita de Ramsey*, which took place on July 30^{th.}, 2015, in the Cinvestav (Mexico) Mathematics Department Student Seminar Summer Talks. - Slides from the talk
*Strongly summable ultrafilters in forcing extensions*, which took place on July 26^{th.}, 2014 within the 29^{th.}Summer Conference on Topology and its Applications. - Slides from my talk
*Ultrafilters and Ramsey-type theorems*, which took place on March 20^{th.}, 2014 at UNAM. - Slides from the talk
*Forcing and the Continuum Hypothesis*, which took place on March 19^{th.}, 2014 at the Cinvestav Mathematics Department. - Slides from the talk
*Some results concerning strongly summable ultrafilters on abelian groups*, which took place on March 16^{th.}, 2014 within the 48^{th.}Spring Topology and Dynamics Conference. - Slides from the talk
*On collectionwise Hausdorff spaces*, which took place on November 4^{th.}, 2009, on the Seventh "Jornadas de Topología". - Slides from my talk
*A problem of algebra which turned out to be undecidable*, which took place on October 13^{th.}, 2009, at the XLII National Congress of the Mexican Mathematical Society. My notes on Whitehead's problem are the result of preparing this talk. - Slides from my talk
*On Carmichael numbers*, which took place on October 23^{th.}, 2008, at the XLI National Congress of the Mexican Mathematical Society. - Slides from my talk
*Applications of Bernoulli numbers in Number Theory*, which took place on April 24^{th.}, 2008, at the Secon Latin American Congress for Mathematics Students.

- My Ph. D. Dissertation Proposal .
- This is the Syllabus , as well as the slides , for my Dissertation
Subject Oral Examination, which took place on December 18
^{th.}, 2012. - My master's
thesis , written under the supervision of
Fernando Hernández
Hernández, defended on August 13
^{th.}, 2010, and the corresponding slides .- Erratum of my master's thesis (if you find any typo or
other kind of erratum, please let me know at
`dfernandezb [at] ipn [dot] mx`).

- Erratum of my master's thesis (if you find any typo or
other kind of erratum, please let me know at
- A little tale that I wrote , or rather wrote itself by means of my hand, on a day in which I was not able to think clearly.
- Mi B. A. thesis , written under the supervision of
Pablo Lam Estrada, and the
slides that I made for its defense, which took place on May 29
^{th.}, 2008.- Erratum of my thesis (if you find a typo or other kind of
erratum, you can let me know at
`dfernandez b [at] ipn [dot] mx`).

- Erratum of my thesis (if you find a typo or other kind of
erratum, you can let me know at