1. [in preparation] Gómez, S., González, I., Hansberg, A., Matos-Wiederhold, T., Amoeba trees, 2025+.

2. Wiederhold, P., Matos-Wiederhold, T., Border tracing in oriented adjacency graphs of polygonal tilings with application to objects made of rectangular, triangular or hexagonal tiles, submitted to Theoretical Computer Science, 2025.

3. Matos-Wiederhold, T., Salvetti, L., Uncountable sets and an infinite linear order game, accepted for publication in Topology Proceedings, 2025.

4. Eslava, L., Hansberg, A., Matos-Wiederhold, T., Ventura, D., New recursive constructions of amoebas and their balancing number, accepted for publication in Aequationes Mathematicae, 2025.

5. Caro, Y., González, I., Hansberg, A., Jácome, M., Matos-Wiederhold, T., A. Montejano, Graphs with constant balancing number, published in Procedia Computer Science, 2023.

6. Matos-Wiederhold, T., An alternative to back-and-forth, published in Topología y sus Aplicaciones, 2020.

Dissertations

1. The Open Coloring Axiom, MSc thesis, 2021. Advisor: Dr. Roberto Pichardo Mendoza.

2. Aplicaciones del lema de Rasiowa-Sikorski a la teoría de órdenes parciales y a la teoría de Ramsey, BSc thesis [in Spanish], 2019. Advisor: Dr. Roberto Pichardo Mendoza.

Set theory/topology

1. This paper proves that zero-dimensional spaces are homeomorphically determined by the isomorphism class of their lattice of uniform topologies. The general case for completely regular spaces is Problem 3.18.

Descriptive combinatorics

2. In this paper, it is proved that if you color the complete graph on the reals in a Baire-measurable fashion where each color class is non-meager, you can find a color-consistent member of a family of graphs where each blown-up clique is a Cantor set. The Lebesgue-measure analog of this (non-meager is replaced by non-null) is unknown, and some hints are provided in the paper.

3. Is there a locally checkable problem that admits a Lebesgue-measurable solutions but no Baire-measurable ones? Problem 2.14.

4. Is the (un-pointed) Cantor topological conjugacy relation Borel? How complex is it? [Solved, it is Borel, 2023+].

Ramsey theory

5. A Ramsey-like result for small-dimensional simplices is proved here. The general case for higher dimensions is unknown and likely uses different techniques.

6. Page 6 of this proves that there are 2-adequate patterns mod m and Lemma 1 of this paper proves there are n-adequate patterns mod 2. When are there n-patterns mod m?

7. Any finite coloring of the integers produces monochromatic sets of the form {x, y, xy, x+y}. [Solved in 2022].