Carlos Matheus

Carlos Matheus is a Brazilian mathematician known for contributions to dynamical systems, Teichmüller dynamics, and ergodic theory. He has held positions at institutions in Brazil, France, and the United States and collaborated with researchers from diverse mathematical centers. His work connects areas represented by prominent figures and institutions across Europe and the Americas.

Early life and education

Matheus was born in Brazil and pursued undergraduate studies at the Federal University of Pernambuco before undertaking graduate research at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) and in France under supervision in programs associated with École Normale Supérieure and University of Paris-Sud (Paris XI). During his doctoral period he interacted with scholars linked to the legacy of Jean-Christophe Yoccoz, alongside networks connected to Michel Herman, Dennis Sullivan, and researchers at the Centre National de la Recherche Scientifique (CNRS). His formative training included exposure to seminars at IHES, colloquia associated with Société Mathématique de France, and collaborations with participants from Universidade de São Paulo and Universidade Federal do Rio de Janeiro.

Mathematical career and research

Matheus’s research program bridges themes from the traditions of Ergodic theory and Teichmüller space studies developed by figures such as William Thurston, Howard Masur, and Alex Eskin. He has published joint work with authors connected to schools at IMPA, Université Paris-Sud, Princeton University, and University of Chicago. His career includes postdoctoral and faculty appointments that placed him in contact with groups at University of California, Berkeley, Columbia University, Université de Lyon, and workshops at the Mathematical Sciences Research Institute (MSRI). Matheus’s projects draw on methods introduced by Maryam Mirzakhani, Artur Avila, and Sebastian Gouëzel, and engage problems studied at conferences such as the International Congress of Mathematicians and meetings organized by the American Mathematical Society (AMS).

Major results and contributions

Matheus contributed to classification problems in the dynamics of interval exchange transformations and translation surfaces, linking to results by Kerckhoff, Masur, Smillie, and Veech. He proved statements concerning Lyapunov spectra in the spirit of work by Forni and Zorich, with techniques related to those of Kontsevich and Zorich on the Hodge bundle over moduli spaces studied by Deligne and Mumford. His collaborations established rigidity phenomena akin to breakthroughs by Eskin and Mirzakhani and produced effective criteria that resonate with invariants introduced by McMullen and Calta. Matheus’s contributions include explicit constructions of pseudo-Anosov maps connected to notions developed by Thurston and applications to counting problems influenced by Eskin–Okounkov enumerative approaches. He has also advanced spectral and cohomological techniques paralleling work of Avila, Gouëzel, and Forni and engaged with questions related to Lagrange spectra studied historically by Markov and Hurwitz.

Awards and honors

Matheus has received recognition from national and international mathematical organizations, including prizes and invitations associated with IMPA programs, fellowships linked to CNRS collaborations, and invited lectures at venues such as MSRI, IHES, and the Clay Mathematics Institute. He has been invited to present plenary and invited talks at meetings organized by the Brazilian Mathematical Society and the European Mathematical Society and has participated in research programs sponsored by the Simons Foundation and the National Science Foundation.

Selected publications and lectures

Selected works include articles and lecture series coauthored with researchers from IMPA, Université Paris-Sud, Princeton University, and ETH Zurich, appearing in journals and proceedings frequented by contributors to the literature of dynamical systems and moduli spaces such as those read by participants of the International Congress of Mathematicians and the AMS colloquia. His recorded lectures have been presented at institutions including MSRI, IHES, IMPA, University of Cambridge, and University of Chicago, and his papers have been cited by authors working in contexts related to Teichmüller theory, interval exchange transformations, and the study of translation surfaces by researchers like Eskin, Forni, and Zorich.

Category:Brazilian mathematicians Category:Dynamical systems theorists