Researcher · UFRO
Israel Morales
Assistant Professor
Department of Mathematics and Statistics · Universidad de La Frontera
Biography
Israel Morales is an Assistant Professor in the Department of Mathematics and Statistics at Universidad de La Frontera (Temuco, Chile), a position he has held since March 2024. He obtained his Ph.D. in Mathematical Sciences at the Centro de Ciencias Matemáticas, UNAM and UMSNH (Mexico) in 2020, with a dissertation entitled «Acciones simpliciales de grupos modulares de superficies de tipo infinito», under the supervision of Dr. Ferrán Valdez Lorenzo. Prior to joining UFRO, he held two postdoctoral positions at the Instituto de Matemáticas-Oaxaca, UNAM: first with CONACyT funding (March 2021–June 2022) and then with DGAPA funding (September 2022–February 2024).
His research specializes in the study of mapping class groups of infinite-type surfaces, known in recent literature as big mapping class groups, with particular interest in rigidity phenomena of simplicial and geometric actions, as well as algebraic and topological properties of these groups. His work draws on tools from geometric group theory, dynamics on flat surfaces, algebraic topology and descriptive set theory.
Research Areas
Big mapping class groups
Homeomorphisms of surfaces
Quasimorphisms
Geometric Group Theory
Riemann and Klein surfaces
Dynamics on flat surfaces
Publications
Realising countable groups as automorphisms of origamis on the Loch Ness monster
Arch. Math. (Basel) Vol. 120 (2023), no. 4, 355–360.
Loxodromic elements in big mapping class groups via the Hooper-Thurston-Veech construction
Algebr. Geom. Topol. Vol. 22 (2022), no. 8, 3809–3854.
Conjugacy classes of big mapping class groups
J. Lond. Math. Soc. (2) Vol. 106 (2022), no. 2, 1131–1169.
Parabolicity of zero-twist tight flute surfaces and uniformization of the Loch Ness monster
Lobachevskii J. Math. Vol. 43 (2022), no. 1, 10–20.
The Alexander method for infinite-type surfaces
Michigan Math. J. Vol. 68 (2019), no. 4, 743–753.
Isomorphisms between curve graphs of infinite-type surfaces are geometric
Rocky Mountain J. Math. Vol. 48 (2018), no. 6, 1887–1904.
Research Grants
FONDECYT · 3240229
Big mapping class groups, origami and dessin d'enfants of infinite type
Outreach and Extension
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