David J. Fernández Bretón -- Curriculum

Since Fall 2021: Assistant Professor, Instituto Politécnico Nacional.
Fall 2020-Winter 2021: Adjunct Professor, Instituto Politécnico Nacional.
Fall 2019-Summer 2021: DGAPA Postdoctoral Fellow, Instituto de Matemáticas, Universidad Nacional Autónoma de México.
Winter 2019-Fall 2020: Adjunct Professor, Instituto Tecnológico y de Estudios Superiores de Monterrey.
Winter-Summer 2019: Postdoctoral Researcher, Departmento de Matemáticas, Centro de Investigación y Estudios Avanzados (Cinvestav).
Fall 2018: Postdoctoral Researcher, Kurt Gödel Research Center for Mathematical Logic, University of Vienna.
Fall 2015-Summer 2018: Post-Doc Assistant Professor, Department of Mathematics, University of Michigan.

(September 2010-January 2015): Ph. D. in Mathematics and Statistics, York University. Thesis defended on December 15, 2014.
Thesis title: Strongly Summable Ultrafilters: Some properties and generalizations.
Thesis supervisor: Juris Steprāns.
(August 2008-January 2010): M.A. in Mathematical Sciences; Joint Graduate Program in Mathematical Sciences UNAM-UMSNH. Degree awarded on August 13^th., 2010 (with Honours).
(February 2005-January 2009): Pasante (i.e. coursework finished but thesis requirement not yet fulfilled) for a Bachelor's Degree in Philosophy, Universidad Nacional Autónoma de México.
(August 2003-June 2007): Licenciatura (i.e. Bachelor's Degree) in Physics and Mathematics; Instituto Politécnico Nacional. Degree awarded on May 29^th., 2008.

Hindman's Theorem in the hierarchy of Choice Principles, Journal of Mathematical Logic 24 no. 1 (2024), 2350002.
(With Lorenzo Carlucci): The adjacent Hindman's theorem for uncountable groups, Colloquium Mathematicum 173 no. 2 (2023), 273-284.
Using ultrafilters to prove Ramsey-type theorems, American Mathematical Monthly 129 no. 2 (2022), 116-131.
(With Nicholas G. Vlamis, and an appendix also with Mathieu Baillif): Ends of non-metrizable manifolds: a generalized bagpipe theorem, Topology and its Applications 310 (2022), 108017.
(With Gerardo Acosta): Equicontinuous mappings on finite trees, Fundamenta Mathematicae 254 no. 2 (2021), 215-240.
(With Joshua Brot and Mengyang Cao): Finiteness classes arising from Ramsey-theoretic statements in set theory without choice, Annals of Pure and Applied Logic 172 no. 6 (2021), 102961.
(With Sung Hyup Lee): Hindman-like theorems with uncountably many colours and finite monochromatic sets Proceedings of the American Mathematical Society 148 no. 7 (2020), 3099-3112.
Stable ordered union ultrafilters and $\mathrm{cov}(\mathcal{M})<\mathfrak c$, Journal of Symbolic Logic 84 no. 3 (2019), 1176-1193.
(With Elizabeth Lauri), A characterization of the Boolean Prime Ideal theorem in terms of forcing notions, Fundamenta Mathematicae 245 no. 1 (2019), 25-38.
(With Michael Hrušák): A parametrized diamond principle and union ultrafilters, Colloquium Mathematicum 153 no. 2 (2018), 261-271.
Hindman's Theorem is only a countable phenomenon, Order 35 (2018), 83-91.
(With Assaf Rinot), Strong failures of higher analogs of Hindman's theorem, Transactions of the American Mathematical Society 369 no. 12 (2017), 8939-8966.
(With Michael Hrušák), Corrigendum to "Gruff ultrafilters" [Topol. Appl. 210 (2016) 355--365], Topology and its Applications 231 (2017), 430-431.
(With Michael Hrušák), Gruff ultrafilters, Topology and its Applications 210 (2016), 355-365.
(With Martino Lupini), Strongly productive ultrafilters on semigroups, Semigroup Forum 92 (2016), 242-257.
Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property, Canadian Journal of Mathematics 68 (2016), 44-66.
Every strongly summable ultrafilter on $\bigoplus\mathbb Z_2$ is sparse, New York J. Math. 19 (2013), 117-129.

Seminar: Equicontinuity of dynamical systems on trees (Equicontinuidad de sistemas dinámicos sobre árboles), Topology Seminar, UAM-Iztapalapa (January 2022).
Seminar: Independence proofs, what are they (good for)? (Pruebas de independencia: ¿Qué son y para qué sirven?), Mathematics Seminar, ESFM-IPN (November 2021).
Keynote lecture: From integral calculus to the mysteries of infinity (Del cálculo integral a los misterios del infinito), via Zoom but officially at Universidad Nacional Federico Villarreal, Peru (October 2021).
Seminar talk: Ramsey theory on infinite additive structures (Teoría de Ramsey en estructuras aditivas infinitas), Combinatorics, Control and Optimization Seminar, Universidad Autónoma Metropolitana - Azcapotzalco (September 2021).
Plenary: Hindman's theorem as a weak version of the Axiom of Choice, Boise Extravaganza in Set Theory 2021, virtual conference (formally held at Boise State University, July 2021).
Parallel session: Ends of non-metrizable manifolds: a generalized bagpipe theorem, Spring Topology and Dynamics Conference 2021, virtual conference (formally held at Murray State University, May 2021).
Parallel session: Uncountable restrictions/extensions of Hindman's theorem (Restricciones y extensiones no numerables del teorema de Hindman), Congreso Nacional Virtual de la Sociedad Matemática Mexicana 2020 (October 2020).
Parallel session talk: Finiteness classes inspired by Ramsey theory in choiceless set theory, special session on "Forcing and Ramsey theory" of the 2020 North American Annual Meeting of the Association for Symbolic Logic, UC Irvine (originally planned for March 2020, cancelled due to the Covid-19 pandemic, and carried out remotely via a talk repository).
Colloquium talk: Additive combinatorics and Ramsey theory from a set-theoretic viewpoint (Combinatoria aditiva y teoría de Ramsey desde la perspectiva de la teoría de conjuntos), Department Colloquium of the Instituto de Matemáticas, Universidad Nacional Autónoma de México (February 2020).
Colloquium talk: Additive combinatorics and Ramsey-type theorems in infinite structures (Combinatoria aditiva y teoremas de tipo Ramsey en estructuras infinitas), Colloquium of the Joint Graduate Program in Mathematical Sciences UNAM-UMSNH, Universidad Nacional Autónoma de México Campus Morelia (November 2019).
Seminar talk: Teoremas de tipo Ramsey en combinatoria aditiva (Ramsey-type theorems in additive combinatorics), "Seminario Súmate", Faculty of Sciences, Universidad Nacional Autónoma de México (August 2019).
Plenary talk: Una generalización del teorema de la gaita (a generalization of the bagpipe theorem), X Jornadas de Topología, Universidad Juárez Autónoma de Durango (May 2019).
Seminar talk: Algebraic Ramsey-theoretic results with small monochromatic sets, Bar-Ilan University Set Theory Seminar, Israel (November 2018).
Plenary talk: Variations on a theme: Hindman's theorem, BLAST 2018, University of Denver (August 2018).
Seminar talk: Partition theorems on uncountable abelian groups, Toronto Set Theory Seminar, Fields Institute (April 27^th., 2018).
Single session talk: Ramsey theory of uncountable abelian groups; Ultrafilters, Ramsey Theory and Dynamics workshop, Université Lyon 1, France (November 24^th., 2017).
Semi-plenary talk: Algebraic Ramsey-theoretic statements with an uncountable flavour, Second Pan Pacific International Conference in Topology and Applications, Busan, South Korea (November 14^th., 2017).
Parallel session talk: Strong negations of Hindman's theorem for uncountable FS-sets, AMS Fall Western Sectional Meeting, University of Denver, U.S. (October 8^th., 2016).
Seminar talk: Some results on strongly summable ultrafilters, University of Illinois at Urbana-Champaign Logic Seminar, Illinois, E.U. (February 19^th., 2016)
Seminar talk: A gentle introduction to infinitary Ramsey theory (Una introducción amable a la teoría infinita de Ramsey), Cinvestav (Mexico) Mathematics Department Student Seminar Summer Talks (July 30^th., 2015).
3 days (1 hr. per day) minicourse: Interaction between Ultrafilters and Ramsey-type Theorems (La Interacción entre los Ultrafiltros y los Teoremas de Tipo Ramsey), 3rd. Mexican School on Logic and Sets (Tercera Escuela de Lógica y Conjuntos), Zacatlán, Puebla, Mexico (November 24-26, 2014).
Parallel session talk: Strongly summable ultrafilters in forcing extensions, 29^th. Summer Conference on Topology and its Applications, College of Staten Island -- City University of New York, Staten Island NY, U.S. (July 26^th., 2014).
Seminar talk: Forcing and the Continuum Hypothesis, Cinvestav Mathematics Department Students' Seminar (March 19^th., 2014).
Parallel session talk: Some results concerning strongly summable ultrafilters on abelian groups, 48^th. Spring Topology and Dynamics Conference, University of Richmond, Richmond VA, U.S. (March 16^th., 2014)

Below is a brief summary of my teaching experience. A more detailed account can be found in the Teaching section.

Instituto Politécnico Nacional: Since October 2020 I have been teaching various courses at both the undergraduate and graduate level (during my first year as an adjunct professor, and subsequently as an assistant professor).
Universidad Nacional Autónoma de México: During the Winter semester in 2020, while I was a postdoc at the Instituto de Matemáticas, I taught a graduate course.
Instituto Tecnológico y de Estudios Superiores de Monterrey: From January 2019 to December 2020, I taught three different courses (for a total of 6 sections) as an adjunct professor.
University of Michigan: From September 2015 through July 2018, while I was a postdoc, I taught five different courses (for a total of 13 different sections); two of these courses were graduate-level.
York University: From September 2010 through August 2014, while I was a PhD student, I helped teach numerous classes as a teaching assistant. Afterwards, during the Fall semester in 2014, I had the chance to be the course director for a class at the Glendon Campus.

June 17-19, 2021: Boise Extravaganza in Set Theory 2021, virtual conference (formally held at Boise State University).
May 12-15, 2021: Spring Topology and Dynamics Conference 2021, virtual conference (formally held at Murray State University).
August 4-9, 2019: Workshop on Set Theory of the Reals, Casa Matemática Oaxaca, affiliated to BIRS.
May 1-3, 2019: X Jornadas de Topología, Universidad Juárez del Estado de Durango, Durango, Mexico.
August 6-10, 2018: BLAST 2018, University of Denver.
November 20-24, 2017: Ultrafilters, Ramsey Theory and Dynamics workshop, Université Lyon 1, France.
November 13-17, 2017: Second Pan Pacific International Conference in Topology and Applications, Busan, South Korea.
October 8-9, 2016: AMS Fall Western Sectional Meeting, University of Denver, U.S.
September 11-16, 2016: Workshop on Set Theory and its Applications in Topology, Casa Matemática Oaxaca, affiliated to BIRS.
March 13-15, 2014: 48^th. Spring Topology and Dynamics Conference, University of Richmond, Richmond, Virginia, U.S.
May 8-11, 2013: Association for Symbolic Logic North American Annual Meeting, University of Waterloo; Waterloo, Canada.
July-December, 2012: Thematic Program on Forcing and its Applications, Fields Institute; Toronto, Ontario, Canada. Among the numerous events included in this thematic semester are:
- 12-16 November, 2012: Workshop on Iterated Forcing and Large Cardinals.
- 22-26 October, 2012: Workshop on Forcing Axioms and their Applications.
December 10-12, 2011: Canadian Mathematical Society Winter Meeting; York University and Ryerson University; Toronto, Canada.
March 21-25, 2011: Fourth Young Researchers in Set Theory Workshop; Königswinter near Bonn, Germany.
October 14-19, 2007: XL National Congress of the Mexican Mathematical Society; UANL.
October 23-28, 2005: XXXVIII National Congress of the Mexican Mathematical Society; IPN.
July 11-22, 2005: Advanced Summer School; Physics Department, Cinvestav.

I have served as referee for the following journals:
I have also been an evaluator for:
- Proposals for conferences requesting funding from the Consejo Nacional de Ciencia y Tecnología (Conacyt), which is the main funding agency in Mexico.
- Undergraduate theses participating for the Sotero Prieto prize to the best undergraduate thesis in mathematics, awarded by the Mexican Mathematical Society.
- Grant proposals for the SEP-CONACyT-ANUIES-ECOS Mexico-France agreement for scientific and technologic research.
I have been a committee member for the following theses:
- Combinatorial Properties of Filters and Ideals, by Jonathan Cancino Manríquez (PhD thesis, defended December 2021); Universidad Nacional Autónoma de México.
- Un acercamiento al invariante cardinal $\mathfrak h$, by René Leonardo Ahumada Lemus (undergraduate thesis, defended September 2021); Universidad Nacional Autónoma de México.
- Aplicaciones de Lógica Matemática en Geometría Algebraica Real: Los Problemas X y XVII de Hilbert, by Luis Edmundo Gatica Norato (undergraduate thesis, defended September 2020); Instituto Tecnológico Autónomo de México.
- Propiedades Combinatorias de los Ideales y el orden de Katĕtov, by José de Jesús Pelayo Gómez (PhD thesis, defended September 2018); Universidad Nacional Autónoma de México.
- Combinatoria Infinita y Teoremas Tipo Ramsey, by Jareth Zuleyca Torres Reyes (undergraduate thesis, defended December 2015); Universidad Nacional Autónoma de México.
I have the following experiences supervising undergraduate students on research projects:
- In the summers of 2016, 2017 and 2018, I supervised undergraduate students (one on each of 2016, 2017, and two in 2018) on research projects as part of the REU (Research Experience for Undergraduates) program.
- In the summer of 2014 I helped Matthias Neufang and Juris Steprāns supervise four students at the Fields Institute Undergraduate Summer Research Program, working on the project titled Metric Arens irregularity.
I have organized, for two years in a row, the virtual conference Interacciones en la Frontera, which toow place June 3-5, 2020 via Bluejeans; and then again May 17-19, 2021, via Zoom.
I was an invited panelist for the discussion The impact of class size on instructors, University of Michigan Seminar on Teaching Mathematics, October 24, 2016.
From September 2015 through June 2018 I was the organizer of the Michigan Logic Seminar at the Department of Mathematics, University of Michigan; and from September 2019 to March 2020 I organized the Mexico City Logic Seminar at the Instituto de Matem\'aticas, UNAM.
I have spoken three times (title of the talks: Surreal Numbers, Ramsey Theory, and What does "infinitely many" mean?) at the Michigan Math Club, a series of weekly talks aimed at advanced undergraduate students.
I am a member of the Association for Symbolic Logic and of the Canadian Mathematical Society since 2013, as well as of the American Mathematical Society since 2014.
Service work as "editor" (meaning I have some administrative privileges) for El Irracional, a MathOverflow/MathStackExchange-like website for mathematical questions (and their answers) in Spanish language.
I completed the Teaching Assistant Certificate of Teaching (TACT), offered by the Teaching Commons at York University, which is certified and endorsed by the Staff and Educational Development Association (SEDA).
I have also participated in teaching-focused events, such as the Teaching in Focus conferences in 2013 y 2014, and the STAY (Supporting Teaching At York) symposia, also in 2013 y 2014.
I know some C programming language, and I can write reasonable code in HTML and CSS (I wrote the code for this webpage myself, and it even incorporates a tiny bit of JavaScript).
I can speak, read and write in Spanish (native language), English (TOEFL score 657), and French (DELF B2 score 82.5/100).
I published the expository article "Un problema de álgebra que resultó indecidible", in Juan Angoa et. al. (eds.), Topología y Sistemas Dinámicos IV, Benemérita Universidad Autónoma de Puebla, 2011; pp. 91-112.

[Zbl 07303626] Hindman, N. and Pleasant, K.; Central sets theorem for arbitrary adequate partial semigroups. Topol. Proc. 58 (2021), 183-206.
[MR4030955] Tachtsis, E.; Łoś's theorem and the axiom of choice. MLQ Math. Log. Q. 65 (2019), no. 3, 280-292.
[Zbl 07150826] Chentsov, A. G.; Bitopological spaces of ultrafilters and maximal linked systems. (English. Russian original) Proc. Steklov Inst. Math. 305, Suppl. 1, S24-S39 (2019); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 24, No. 1, 257-272 (2018).
[Zbl 06908765] Xu, X.; Liang, M.; and Luo, H.; Ramsey theory. Unsolved problems and results.. De Gruyter (ISBN 978-3-11-057651-1/hbk; 978-3-11-057670-2/ebook). xii, 178 pp. Berlin, 2018.
[MR3941152] Mermelstein, O.; Calculating the closed ordinal Ramsey number $R^{cl}(\omega\cdot 2,3)$.. Israel J. Math. 230 (2019), no. 1, 387-407.
[MR3835077] Tachtsis, E.; On the set-theoretic strength of Ellis' theorem and the existence of free idempotent ultrafilters on $\omega$. J. Symb. Log. 83 (2018), no. 2, 551-571.
[MR3700856] Brendle, J.; Q. Sets and computations (Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 33), NJ, 2018, pp. 1--10.
[Zbl 06735264] Guerrero Sánchez, D; Tkachuk, V. V.; If $C_p(X)$ is strongly dominated by a second countable space, then $X$ is countable. J. Math. Anal. Appl. 454 no. 2 (2017), 533-541.
[MR3633221] Viale, M.; Forcing the truth of a weak form of Schanuel's conjecture. Confluentes Math. 8 (2016), no. 2, 59-83.
[MR3552290] Juhász, I.; Soukup, L.; and Szentmiklóssy, Z.; Pinning down versus density. Israel J. Math. 215 (2016), no. 2, 583–605.
[Zbl 06506061] Shelah, S.; Spinas, O.; Mad spectra. J. Symb. Log. 80 (2015), 901-916.
[Zbl 06517543] Dow, A.; Generalized side-conditions and Moore-Mrówka. Topology Appl. 197 (2016), 75-101.
[MR3459883] Herrlich, H.; Howard, P.; and Tachtsis, E.; On a certain notion of finite and a finiteness class in set theory without choice. Bull. Pol. Acad. Sci. Math. 63 no. 2 (2015), 89-112.
[MR3433520] Gavryushkin, A.; Khoussainov, B.; and Stephan, F.; Reducibilities among equivalence relations induced by recursively enumerable structures. Theoret. Comput. Sci. 612 (2016), 137-152.
[MR3377354] Spinas, O. and Wyszkowski, M.; Silver Antichains. J. Symb. Log. 80 (2015), 503-519.
[Zbl 1328.03052] Usuba, T.; Characters of countably tight spaces and inaccessible cardinals. Topology Appl. 161 (2014), 95-106.

Honorific Mention, Sotero Prieto Prize to the best Undergraduate Thesis in Mathematics 2008, awarded by the Mexican Mathematical Society.
I participated in the National Mathematics Contest "Pierre Fermat" (organized by Insituto Politécnico Nacional in Mexico) in 2002 in the High School category, and from 2003 to 2006 in the Undergraduate category. I made it to the finals in 2002, 2003 and 2004; earned third place in 2005 and first place in 2006.
Second best GPA among all Philosophy Majors, Class of 2006-2009; FFyL-UNAM.

Curriculum Vitae

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Personal Information

Employment History

Education

(Published/Accepted) Research Papers

Submitted preprints

Invited Talks

Teaching Experience

Conferences Attended

Miscellaneous

Reviews for Mathematical Reviews (MathSciNet) or Zentralblatt

Awards