Dr. Gerardo HernandezDuenas
Associate Professor
Institute of Mathematics
Unit Juriquilla
UNAM
Office: 2
Institute of Mathematics
UNAM Campus Juriquilla
Blvd Juriquilla # 3001
76230 Juriquilla, Querétaro, México
Phone: (52) 4421926287
Email: hernandez at im dot unam dot mx
Associate Professor
Institute of Mathematics
Unit Juriquilla
UNAM
Office: 2
Institute of Mathematics
UNAM Campus Juriquilla
Blvd Juriquilla # 3001
76230 Juriquilla, Querétaro, México
Phone: (52) 4421926287
Email: hernandez at im dot unam dot mx
I did my undergraduate studies at the Departamento de Matemáticas  Universidad de Guanajuato under the supervision of my undergraduate thesis adivser Xavier GómezMont Ávalos. I obtained my Ph. D. degree at the Department of Mathematics at The University of Michigan  Ann Arbor. My Ph. D. advisers were Alejandro Uribe and Smadar Karni. I was a Van Vleck visiting scholar (Posdoc position) at the Department of Mathematics at the University of Wisconsin  Madison. I worked with my posdoc advisers Leslie M. Smith and Samuel N. Stechmann.
Research areas:

Applied Mathematics and Atmospheric Sciences

Numerical Analysis and Hyperbolic Conservation Laws

Geophysical Fluid Dynamics

Semiclassical Analysis

Turbulence
I am interested in both theory and numerics of mathematical models based on Partial Differential Equations. In the theoretical part, I study models derived from physical laws with applications to Atmospheric Sciences, Geophysical Fluid Dynamics and Physics. A variety of models can be derived from the NavierStokes equations or similar by assymotic arguments or by assuming simplifying conditions. Such models are to maintain a balance between reality and model complexity. Examples include: shallow water equations, blood flow models, Boussinesq equations, quasigeostrophic equations, anelastic equations and simplifications to model precipitating turbulent convection, among others.
In Mathematical Physics, I am also interested in Schrodingertype operators. In particular, I work on techniques developed in Semiclassical Analysis for Pseudodifferential operators.
In numerical analysis, I am interested in developping efficient numerical methods to implement a variety of models. Models in the category of Hyperbolic Conservation laws may encounter numerical difficulties achieving stability or reaching convergence to the entropysatisfying solutions in the presence of shock waves. In Geophysical Fluid Dynamics, one may need to use different techniques such as pseudospectral methods to analyze different types of waves interacting in an atmospheric phenomenon and ensuring that the solution satisfies the continuity equation when appropriate, etc.
Erdős number: 4
Me  Andrew J. Majda  Charles Louis Fefferman  J. Marshall Ash  Paul Erdős1
Me  Andrew J. Majda  Charles Louis Fefferman  J. Marshall Ash  Paul Erdős1