I am an associate professor at the Department of Mathematics, University of Concepción, Chile.
I am currently the Director of our Master's Program in Mathematics.
Research:
I'm interested in mathematical logic, broadly speaking, particularly set theory.
I currently work with cardinal characteristics of the continuum, Aronszajn trees, and I have also explored connections with number theory through Hilbert's Tenth Problem.
I completed my PhD at University of Toronto in 2010 under Stevo Todorcevic. From 2011-2013 I was a postdoctoral fellow at UNAM, campus Morelia. From 2013-2017 I was an assistant professor at University of Concepcion.
Existential decidability for addition and divisibility in holomorphy subrings of global fields, (with Javier Utreras, Xavier Vidaux)
Journal of Number Theory 241 (2022), 504-530.
arXiv:2010.14024
Hereditary Intervals Algebras and Cardinal Characteristics of the Continuum, (with M. Hrušák, A. Ramos-García)
Israel J. Math. 242 (2) 2021, no. 2, 769-795.
arXiv:1905.13398
The diophantine problem for addition and divisibility for subrings of rational functions over finite fields. (with L. Cerda-Romero)
Proyecciones, vol 39, no. 3 (2020), 721--735.
Link to paper
Undecidability of \(\mathbb Q^{(2)}\), (with J. Utreras, C. Videla)
Proc. Amer. Math. Soc. 148 (2020), 961-964
arXiv:1809.04670
On a construction of Malykhin. (with A. Ramos-García)
Topology Proceedings 53 (2019), 209--218.
Link to paper
The Diophantine problem for addition and divisibility over subrings of the rationals. (with L. Cerda-Romero)
J. of Symb. Logic 82 (2017), no. 3, 1140--1149.
Link to paper
Generic existence of MAD families. (with O. Guzmán-González, M. Hrušák, A. Ramos-García)
J. of Symb. Logic 82 (2017), no. 1, 303--316.
Link to paper
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