Man

Enrique Gonzalo Reyes Garcia

Associate Professor

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

Líneas de Investigación


Mathematical Physics, Differential Equations, Differential Geometry

Educación

  •  Mathematics, MCGILL UNIVERSITY. Canada, 1999
  •  Mathematics, PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE. Chile, 1988
  •  Mathematics, University of Saskatchewan. Canada, 1993

Experiencia Académica

  •   Faculty Lecturer Part Time

    PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE

    Matemáticas

    Santiago, Chile

    1989 - 1989

  •   Research Assistant Part Time

    University of Saskatchewan

    Arts and Science

    Saskatoon, Canada

    1991 - 1994

  •   Faculty Lecturer Part Time

    MCGILL UNIVERSITY

    Arts and Science

    Montreal, Chile

    1994 - 1998

  •   Visiting Assistant Professor Full Time

    Utah State University

    Arts and Science

    Logan, Estados Unidos

    1998 - 1999

  •   Faculty Lecturer Part Time

    Yale University

    Arts and Science

    New Haven, Chile

    2000 - 2001

  •   Visiting Assistant Professor Full Time

    University of Oklahoma

    Arts and Science

    Norman, Estados Unidos

    2001 - 2003

  •   Associate Professor Full Time

    UNIVERSIDAD DE SANTIAGO DE CHILE

    Ciencia

    Santiago, Chile

    2003 - At present

  •   Postdoctoral Researcher Full Time

    University of Minnesota

    Arts and Science

    Minneapolis, Estados Unidos

    1999 - 1999

  •   Postdoctoral Researcher Full Time

    Centre de recherches mathematiques

    n/a

    Montreal, Canada

    1999 - 1999

  •   Postdoctoral Researcher Full Time

    YALE UNIVERSITY

    Arts and Science

    New Haven, Estados Unidos

    2000 - 2001

Experiencia Profesional

  •   Associate Professor Full Time

    Universidad de Santiago de Chile

    Santiago, Chile

    2003 - At present

  •   Visiting Assistant Professor Full Time

    University of Oklahoma

    Norman, Estados Unidos

    2001 - 2003

  •   Faculty Lecturer Part Time

    Yale University

    New Haven, Estados Unidos

    2000 - 2001

  •   Visiting Assistant Professor Full Time

    Utah State University

    Logan, Estados Unidos

    1998 - 1999

  •   Faculty Lecturer Part Time

    McGill University

    Montreal, Canada

    1994 - 1998

  •   Teaching Assistant Part Time

    University of Saskatchewan

    Saskatoon, Canada

    1991 - 1994

  •   Faculty Lecturer Part Time

    Pontificia Universidad Catolica de Chile

    Santiago, Chile

    1989 - 1989

Formación de Capital Humano


THESIS ADVISING
1. (Advisor) “Introduction to the Yamabe Problem". Honors Thesis written by Christian Andre Droguett-Aguila, Universidad de Santiago de Chile, 2005.

2. (Advisor) “The Gauss-Bonnet-Chern Theorem". Master of Science Thesis written by Rodrigo Quezada Aguayo, Universidad de Santiago de Chile, 2013.

3. (Advisor) “Central extensions and Manin triples for algebras of pseudodifferential operators in one
and several variables”. Ph.D. Thesis written by Jarnishs Beltran Mejia, Universidad de Santiago de Chile, 2013.

4. (Advisor) “Some geometric aspects of fluid mechanics". Master of Science Thesis written by Eugenio Rivera Mancilla, Universidad de
Santiago de Chile, 2013.

5. (Advisor) “Newton da Costa structures and their Applications". Master of Science Thesis written by Vidal Navarro Mena, Universidad de Santiago
de Chile, 2013.

6. (Advisor) “Differential graded algebras, A? -algebras and Hodge theory". Master of Science Thesis written by Maria Jose Moreno Silva, Universidad de Santiago de Chile, 2014.

7. (Co-advisor) “Mathematical models of associative learning: an introduction with simulations".
Master of Science Thesis written by Omar Perez Riveros, Universidad de Santiago de Chile, 2013.

PARTICIPATION IN THESIS COMMISSIONS

1. (Member, Thesis Commission) “Periodic orbits and entropy of applications of the interval". M.Sc. Mathematics Thesis written by
Alvaro Castaneda, Universidad de Santiago de Chile, 2006.

2. (Member, Thesis Commission) "Dynamical aspects of König's method." M.Sc. Mathematics Thesis written by Gerardo Honorato,
Universidad de Santiago de Chile, 2006.

3. (Member, Thesis Commission) “Equations ut = uxxxxx + G(u, ..., uxxxx ) describing pseudo-spherical surfaces with
fp1 = ?p f11 + ?p , 2 ? p ? 3". Ph.D. Thesis written by Verissimo Pereira Gomes-Neto, Universidade de Bras?lia, 2010.

4. (Member, Thesis Commission) “Higher order iterative methods on Riemannian manifolds”. Ph.D.
Thesis written by Rodrigo Castro Marin, Universidad de Santiago de Chile, 2011.

5. (Member, Thesis Commission) “On the Cauchy problem for an equation in fractional derivatives". Master of Science
Thesis written by Cristhian Montoya, Universidad de Santiago de Chile, 2012.

6. (Member, Thesis Commission) “The heat kernel on metric spaces with measure and its application to a difusion equation".
Master of Science Thesis written by Jose Ramirez Molina, Universidad de Santiago de Chile, 2013.

7. (Member, Thesis Commission) “The Polya transform method in the study of equations in infinitely many derivatives". Master of Science Thesis written by Ignacio Olea Carrera, Universidad de Chile, 2014.

8. (Member, Thesis Commision) “Stafford Beer’s Team Syntegrity Methodology". Engineering Undergraduate Thesis
written by Benito Contreras Sepulveda, Universidad de Santiago de Chile, 2006.

9. (Member, Thesis Commission) “An introduction to non-euclidean geometry via
Girard’s theorem. An educational perspective". Final Project for a Physics and Mathematics
Secondary Education Teaching Diploma, written by Oscar Barraza Figueroa and Rolando
Reyes Labb ?, Universidad de Santiago de Chile, 2012.

CURRENT GRADUATE STUDENTS

1. Miguel Bezares (M.Sc.) "The Cauchy problem in General Relativity". To graduate on December 2014
2. Gonzalo Palomera (M.Sc.) "Hamiltonian formulation of General Relativity". To graduate on December 2014.
3. Lida Mendoza (Ph.D.) "Categorification results for knots and graphs and some applications". To graduate on December 2014.
4. Samin Cerón (Ph.D.) "Some applications of rational homotopy to the geometry of partial differential equations". To graduate on July 2015.
5. Wilson Arley (Ph.D., co-tutoring) "The Duflo Isomorphism". To graduate on July 2015.
6. Boris Brayovic (Ph.D.) "Geometric aspects of nonlinear supersymmetric equations". To graduate on December 2015.
7. Alvaro Hidalgo (Ph.D.) "Hamiltonian mechanics and Finsler geometry". To graduate on December 2015.
8. Alan Chavez (Ph.D., co-tutoring) "A topological study of Camassa-Holm equation on loop spaces". To graduate July 2016.


Premios y Distinciones

  •   NSERC Postdoctoral Fellowship

    Natural Sciences and Engineering Research Council of Canada

    Canada, 1999

    n/a

  •   J.W. McConnell McGill Major Fellowship

    McGill University, Montreal, Canada

    Canada, 1998

    Graduate Studies Fellowship

  •   Special One-Year Faculty of Science McGill Major Fellowship

    McGill University, Montreal, Canada

    Canada, 1998

    Graduate Studies Fellowship

  •   Graduate Studies Fellowship

    Fonds pour la Formation de Chercheurs et l'Aide a la Recherche (FCAR)

    Canada, 1997

    n/a

  •   David Stewart Memorial McGill Major Fellowship

    McGill University, Montreal, Canada

    Canada, 1996

    Graduate Studies Fellowship

  •   Graduate Studies Fellowship

    Institut des sciences mathematiques, Montreal

    Canada, 1995

    n/a

  •   University of Saskatchewan Scholarship

    University of Saskatchewan

    Canada, 1994

    Graduate Studies Scholarship, during 1992--1994.


 

Article (33)

Equations of Camassa-Holm type and the geometry of loop groups
Sobolev spaces on locally compact abelian groups and the bosonic string equation
Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces
NONLOCAL SYMMETRIES, COMPACTON EQUATIONS, AND INTEGRABILITY
On a General Class of Nonlocal Equations
THE KADOMTSEV-PETVIASHVILI HIERARCHY AND THE MULASE FACTORIZATION OF FORMAL LIE GROUPS
THE RELLICH LEMMA ON COMPACT ABELIAN GROUPS AND EQUATIONS OF INFINITE ORDER
Geometric Integrability of the Camassa-Holm Equation. II
The dual modified Korteweg-de Vries-Fokas-Qiao equation: Geometry and local analysis
The initial value problem for ordinary differential equations with infinitely many derivatives
The modified Hunter-Saxton equation
Equations of Pseudo-Spherical Type (After SS Chern and K. Tenenblat)
Nonlinear Equations with Infinitely many Derivatives
The Modified Camassa-Holm Equation
Completeness in quantum mechanics and the Weyl-Titchmarsh-Kodaira theorem
Functional calculus via Laplace transform and equations with infinitely many derivatives
Remarks on Undecidability, Incompleteness and the Integrability Problem
Nonlocal symmetries and a Darboux transformation for the Camassa-Holm equation
Explicit solutions to the Kaup-Kupershmidt equation via nonlocal symmetries
On nonlocal symmetries of some shallow water equations
Correspondence theorems for hierarchies of equations of pseudo-spherical type
Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equations
The soliton content of classical Jackiw-Teitelboim gravity
Nonlocal symmetries and the Kaup-Kupershmidt equation
On the motion of particles and strings, presymplectic mechanics, and the variational bicomplex
On covariant phase space and the variational bicomplex
On generalized Bäcklund transformations for equations describing pseudo-spherical surfaces
Transformations of solutions for equations and hierarchies of pseudo-spherical type
Geometric integrability of the Camassa-Holm equation
On formal integrability of evolution equations and local geometry of surfaces
Conservation laws and Calapso–Guichard deformations of equations describing pseudo-spherical surfaces
Some geometric aspects of integrability of differential equations in two independent variables
Pseudo-spherical Surfaces and Integrability of Evolution Equations

BookSection (5)

Generalized euclidean bosonic string equations
Jet bundles, symmetries, Darboux transforms
The soliton content of the Camassa-Holm and Hunter-Saxton equations
Integrability of evolution equations and pseudo-spherical surfaces
On geometrically integrable equations and hierarchies of pseudo-spherical type

ConferencePaper (2)

On equations with infinitely many derivatives: integral transforms and the Cauchy problem
The Laplace Transform in the Study of Equations with Infinitely Many Derivatives
55
Enrique Reyes

Associate Professor

Mathematics and Computer Science

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

14
Humberto Prado

Full Professor

Mathemnatics and Computer Sciences

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

1
Guillermo Palma

Academico Jornada Completa

Departamento de Fisica

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile