Jorge Sotomayor Tello

Jorge Manuel Sotomayor Tello
Born	(1942-03-25)25 March 1942 Lima, distrito de Rímac, Peru
Died	7 January 2022(2022-01-07) (aged 79) Rio de Janeiro, Brazil
Resting place	Memorial do Carmo, 285, Caju, Rio de Janeiro
Other names	Soto
Alma mater	Universidad Nacional Mayor de San Marcos, Lima, Perú, Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
Known for	Principal configuration, curvature lines, umbilic points , structural stability of first order, bifurcations of codimension one, two and three.
Spouse	Marilda Sotomayor
Awards	National Order of Scientific Merit Brazilian Academy of Sciences Guggenheim Foundation
Scientific career
Fields	Differential equations, Dynamical Systems, Bifurcation Theory, Differential Equations of Classical Geometry
Institutions	Instituto Nacional de Matemática Pura e Aplicada Universidade de São Paulo Universidade Federal de Itajubá(Visiting Professor)
Thesis	Estabilidade Estrutural de Primeira Ordem e Variedades de Banach  (1964)
Doctoral advisor	Maurício Peixoto
Other academic advisors	José Tola Pasquel

Jorge Manuel Sotomayor Tello (25 March 1942 – 7 January 2022) was a Peruvian-born Brazilian mathematician who worked on differential equations., bifurcation theory, differential equations of classical geometry.

He is the son of Alfonso Sotomayor Ibarra, an accountant, and Clara Rosa Tello de Sotomayor, a housewife. Brother of Vilma, Luis, Carlos and Alfonso. He was married to Marilda Antonia de Oliveira Sotomayor. Father of Leonardo and Mariana.

Sotomayor earned his Ph.D. from the IMPA in 1964 under the supervision of Maurício Peixoto at the age of 22 years.

In the dissertation Estabilidade Estrutural de Primeira Ordem e Variedades de Banach (First order structural stability and Banach manifolds) he presented a geometric reinterpretation and extension of the fruitful notions and results relating bifurcations and stability that were introduced by A. A. Andronov and E. A. Leontovich.

Sotomayor visited the University of California at Berkeley during 1966–1968, where he witnessed the great developments in dynamical systems of that period which took place under the leardship of Stephen Smale.

He was a recipient of Brazil's National Order of Scientific Merit in mathematics. From 1994 until his death in early 2022, he was a member of the Brazilian Academy of Sciences. He also was a Fellow of John Simon Guggenheim Memorial Foundation (1983).

Sotomayor is the author of the textbooks Lições de Equações Diferenciais Ordinárias, IMPA, Projeto Euclides, (1979), Singularidades de Aplicações Diferenciáveis, ELAM (1976) and Curvas Definidas por Equações Diferenciais no Plano, 13^o Colóquio Brasileiro de Matemática, IMPA, (1981). He also translated essays of Henri Poincaré into Portuguese, which were published in a book under the title Um Poeta, um Matemático e um Físico: Três Ensaios Biográficos por Henri Poincaré, EDUSP,(2008).

He is also author of the books Lines of Curvature and Umbilical Points on Surfaces, 18^o CBM, Publicações Matemáticas, IMPA,(1991) with Carlos Gutierrez, reprinted and updated as Structurally Configurations of Lines of Curvature and Umbilic Points on Surfaces, Lima, Monografias del IMCA, (1998) and Differential Equations of Classical Differential Geometry, a Qualitative Theory, 27^o CBM, Publicações Matemáticas,IMPA, (2009) with Ronaldo Garcia.

Introduced, with Carlos Gutierrez, the concept of ``principal configuration`` of curvature lines on surfaces. See Structurally Stable Configurations of Lines of Principal Curvature", Astérisque, França, v. 98–99, p. 195–215, (1982). The ideas leading to his work in this subject—traced back to the classical work of G. Monge, C. Dupin and G. Darboux—are discussed in his essay Monge's Ellipsoid. This research has been elaborared and extended in several directions by Sotomayor and his collaborators to include a large class of the differential equations of classical geometry (for example, the asymptotic lines, the axial curvature lines, the lines of mean curvature) and other classes of manifolds (for example, algebraic surfaces in 3 and 4 four dimensional Euclidean spaces).

Mauricio Peixoto's Testimonial

``It is a pleasure to say a few words in this occasion, commemorating the 60th birthday of Sotomayor. He was my student and got his PhD at IMPA in 1964. At the same time two other IMPA students of mine, Ivan Kupka and Aristides Barreto, also got their doctorates. These were the first doctorates awarded by IMPA. The theses of Sotomayor and Kupka got quick international recognition and were initial steps in the direction of establishing IMPA as a mathematical research institution, strong in Dynamical Systems. Both Sotomayor and Kupka came to IMPA from Peru, Sotomayor through the shortest geodesic and Kupka through an arc with origin in Strasbourg (France). In the wake of Sotomayor a number of Peruvians got their doctorates at IMPA. Among them, Carlos Gutierrez and Cesar Camacho became distinguished mathematicians and professors at IMPA. Currently Camacho is the Director of IMPA.

Sotomayor is certainly one of the pioneers of the modern theory of bifurcation, put in the context of the theory of Dynamical Systems.

This point of view was introduced in his thesis when he considered a 2-dimensional manifold M and on the space of flows on M, Ω(M), he considered an arc γ and studied the intersection γ ᑕ Σ when Σ ᑕ Ω(M) is the set of structurally stable flows on M.

In 1982 Sotomayor, together with C. Gutierrez put the concept of structurally stability in the study of the foliation determined by the lines of principal curvature of an ordinary surface in R³.

This point of view enriched later by the collaboration of R. Garcia and others amounted to a new vision of the classical work of Monge, Dupin, Darboux, Caratheodory.

Let Soto continue to produce for many years to come his beautiful, relevant and down to earth mathematics``.

Death

He passed away on 7 January 2022, at the age of 79.

Selected publications

• Sotomayor, J. (1993). "O elipsóide de Monge" (PDF). Revista Matemática Universitária. 15: 33–47.
• Sotomayor, J. (2007). "El elipsoide de Monge y las líneas de curvatura". Materials Matemàtics. 01: 1–25.
• Sotomayor, J.; Garcia, R. (2016). "Historical Comments on Monge's Ellipsoid and the Confgurations of Lines of Curvature on Surfaces". Antiquitates Mathematicae. 10: 348–354.
• Sotomayor, J. (2019). "A Private Mathematical Lesson, Rio de Janeiro,1933". Nexus Mathematicae. 02: 01–04.
• Sotomayor, J. (2020). "Reminiscences of a Mathematical Sojourn at San Marcos, 1959 - 61, and at IMPA, 1962". Nexus Mathematicae. 03: 01–14. doi:10.5216/nm.v3.63724. S2CID 238106577.
• Sotomayor, J. (2020). "On an encounter of two men of mathematics in Lima". Revista Brasileira de História da Matemática. 20 (40): 01–07. doi:10.47976/RBHM2020v20n4001-07. S2CID 229001686.
• Sotomayor, J. (2020). "On Maurício M. Peixoto and the arrival of Structural Stability to Rio de Janeiro, 1955". An. Acad. Bras. Ciências. 92 (1): 01–07. doi:10.1590/0001-3765202020191219. PMID 32267292. S2CID 215406476.
• Sotomayor, J.; Garcia, R.; Mello, L. (2020). "Maurício M. Peixoto (1921-2019)". Revista Matemática Universitária da SBM. 1: 01–22. doi:10.21711/26755254/rmu202013. S2CID 226539649.
• Sotomayor, J. (1992). "A Caderneta de Geometria". Revista do Professor de Matemática da SBM. 21: 1–5.
• Sotomayor, J. (2018). "Mathematical encounters". ICCM Notices. Notices of the International Congress of Chinese Mathematicians. 06 (2): 94–98. arXiv:1803.10593. doi:10.4310/ICCM.2018.v6.n2.a11. S2CID 119591081.
• Sotomayor, J. (1974). "Generic one-parameter families of vector fields on two-dimensional manifolds". Publications Mathématiques de l'IHÉS. 43: 5–46. doi:10.1007/bf02684365. S2CID 123134043.
• Dumortier, F.; Roussarie, R.; Sotomayor, J. (1987). "Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3". Ergodic Theory and Dynamical Systems. 7 (3): 375–413. doi:10.1017/s0143385700004119.
• "with C. Gutiérrez: Structurally Stable Configurations of Lines of Principal Curvature", Astérisque, França, v. 98--99, p. 195--215, (1982).
• Sotomayor, J. (2021). "An encounter of classical differential geometry with dynamical systems in the realm of structural stability of principal curvature configurations". São Paulo Math.Journal. 16: 256–279. doi:10.1007/s40863-021-00231-6. S2CID 236365729.

External links

• www.ime.usp.br/~sotp(Homepage)
• lattes.cnpq.br/2202693274986226(Lattes CNPq)
• Jorge Sotomayor Tello at the Mathematics Genealogy Project
• Template:Worldcat id
• www.researchgate.net/profile/Jorge-Sotomayor(Researchgate)