Mathematical Physics, Differential Equations, Differential Geometry

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.