Dr. Gerardo Hernandez-Duenas
  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) 442-192-6287
  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 Gómez-Mont 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 Navier-Stokes 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, quasi-geostrophic equations, anelastic equations and simplifications to model precipitating turbulent convection, among others.
 
In Mathematical Physics, I am also interested in Schrodinger-type 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 entropy-satisfying solutions in the presence of shock waves. In Geophysical Fluid Dynamics, one may need to use different techniques such as pseudo-spectral 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