I have conducted research in dynamical systems and low-dimensional topology, focusing on the classification of pseudo-Anosov maps using Markov partitions and their symbolic dynamics. I aim to explore further applications of the symbolic dynamics of pseudo-Anosov maps to the study of the geometry and topology of their mapping tori. Recently, I have been thinking about examples of pseudo-Anosov maps on infinite-type surfaces.
1] Geometric Markov partitions for pseudo-Anosov homeomorphisms with prescribed combinatorics ( arXiv:2409.03066 )
2] A classification of pseudo-Anosov homeomorphisms via geometric Markov partitions (arXiv:2405.06160 )
3] An Algorithmic Classification of Generalized Pseudo-Anosov Homeomorphisms via Geometric Markov Partitions ( PhD thesis arXiv:2405.07954 )
Some Talks
1] Una clasificación de los Grupos de Automorfismos para Dominios $k$-conexos en la Esfera de Riemann ( Aquelarre Matemático )
2] Uso de corrientes en sistemas dinámicos ( IMATE )