Research Interests

Geometric function theory in one and several variables; planar harmonic mappings; differential geometry of curves; real and complex oscillation theory

Curriculum Vitae

Positions

2010-2016

Dean Faculty of Mathematics

2007-2010

Chair Department of Mathematics

1998-2007

Director Graduate Program

2006-  Pontificia Universidad Católica de Chile

Professor

1994-2006 Pontificia Universidad Católica de Chile

Associate Professor

1993-1994 Pontificia Universidad Católica de Chile

Assistant Professor

1990-1993 University of Pennsylvania

Instructor

Education

1990 Ph.D. - Stanford University

Thesis under professor B. Osgood, The Schwarzian derivative in Riemannian geometry, univalence criteria and quasiconformal reflections

1985 M.S. - Pontificia Universidad Católica de Chile

Thesis under professor J. Gevirtz, The mean value theorem for quasi-isometries in Banach Spaces

1984 B.S. - Pontificia Universidad Católica de Chile

Supervised Students

2017

Ignacio Tejeda, On the uniqueness of Ahlfors' Schwarzian in R, Undergraduate Thesis, 2017

2015

Álvaro Ferrada, Affine and linear invariant families of harmonic mappings, Ph.D. 2015

2015

Rodrigo Vargas, Convex mappings and Aleksandrov's measures, Ph.D. 2015

2010

Willy Sierra, John domains on minimal surfaces, Ph.D. 2010

2008

Rodrigo Vargas, Distortion theorems for Nehari's p-criterion, M.S. 2008

2006

Paulina Barriga, Hilbert's metric on convex domains, M.S. 2006

2004

Rodrigo Hernández, The Schwarzian derivative in several complex variables, Ph.D. 2004

2003

Pilar Herreros, Hiperbolic convexity and the theorem of Gehring-Pommerenke, M.S. 2003

Research Grants

2019-2022

Fondecyt Grant 1190830, Applications of the Schwarzian derivative to curves and surfaces, P.I.

2015-2018

Fondecyt Grant 1150115, Harmonic and quasiconformal mappings, P.I.

2011-2014

Fondecyt Grant 1110321, Extensions of harmonic mappings, P.I.

2007-2010

Fondecyt Grant 1071019, The Schwarzian derivative, Weierstrass-Ennper lifts and harmonic mappings, P.I.

2003-2006

Fondecyt Grant 1030589, The Schwarzian derivative for harmonic mappings, P.I.

2003-2006

Fondecyt Grant 1030589, The Schwarzian derivative for harmonic mappings, P.I.

2003-2006

Fondecyt Grant 7030032 for International Cooperation, The Schwarzian derivative for harmonic mappings, P.I.

2000-2002

Fondecyt Grant 1000627, A variational method to study optimal univalence criteria, P.I.

2000-2002

Fondecyt Grant 7000627 for International Cooperation, A variational method to study optimal univalence criteria, P.I.

1997-1999

Fondecyt Grant 1971055, Convexity in geometric function theory and univalence criteria, P.I.

1994-1996

Fondecyt Grant 1940690, Applications of the Schwarzian derivative in analysis and geometry, P.I.

1991-1992

NSF Grant DM 590-01957, Associate Researcher

1991-1992

NSF Grant DM 590-01957, Associate Researcher

Publications

Preprints

Teaching

Other Stuff

GFT in South America 2017

Jhonattan Gaona, Iason Efraimidis, Rodrigo Hernandez, Martin Chuaqui, Alvaro Ferrada, Rodrigo Vargas, Hugo Arbeláez, Willy Sierra