CV



Full Curriculum Vitae (PDF) (Last updated: January/20/2024)

Spanish version (Last updated: January/20/2024)

 

Curriculum Vitae

 

Contact Information:

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

Research Interests:

Applied Mathematics to Atmospheric Sciences
Turbulence: Theory, Numerics and Computations
Numerical Methods for Hyperbolic Conservation Laws
Geophysical Fluid Dynamics
Semiclassical Analysis

Present Position:

National Autonomous University of Mexico- Juriquilla.  Since June, 2014
Institute of Mathematics
Full Professor - Level A
PRIDE Level C

Previous Position:

University of Wisconsin - Madison. June, 2011 - May 2014
Department of Mathematics
Postdoctoral Fellow
Van Vleck Visiting Assistant Professor

Other Academic Positions:

Member of the SIAM Committee on Section Activities. 2024-2026.
Purpose: Review policy matters related to sections, to assist in overseeing section activities, and to make recommendations to the Board on matters pertaining to sections.
https://www.siam.org/about-siam/committees/committee-on-section-activities
 
Officer of the SIAM Activity Group "Mathematics of Planet Earth" (SIAG MPE). 2023-2024.
Member of the Leadership (Secretary)
SIAG/MPE studies Planet Earth, its life-supporting capacity, and the impact of human activities. Topics of interest include weather and climate, the carbon cycle, mathematical ecology, land use, food security, urban infrastructure, energy, water, transportation, the spread of infectious diseases, ecosystem services, extreme events, invasive species, natural disasters, and issues of vulnerability and resilience.
https://www.siam.org/membership/activity-groups/detail/mathematics-of-planet-earth
 
Faculty Adviser of the SIAM Student Chapter at UNAM. 2021-present
Co-Faculty Adviser (in collaboration with Dr. Raul Esquivel) of the first set of officers of the SIAM Student Chapter at UNAM. 
 
President of MexSIAM. 2018-2021
President of the Mexico Section of SIAM, the Society for Industrial and Applied Mathematics. I became the President after reviving the Section with the support of SIAM. SIAM was founded in 1951 and has more than 11,000 members. The Mexico Section, during the period 2018-2021 had more than 130 members. More about MexSIAM and the other 15 Sections around the world at:
http://www.mexsiam.org
 

Education:

University of Michigan. April 21, 2011
Ph.D in Mathematics. Rackham Graduate School
Ann Arbor, Michigan.
- Advisor in pure mathematics: Professor Alejandro Uribe. Email: uribe at umich dot edu
- Advisor in applied mathematics: Professor Smadar Karni. Email: karni at umich dot edu

University of Guanajuato. Aug. 2000 - July 2005
Bachelors Degree in Mathematics: GPA 9.8 / 10.
Guanajuato, Mexico
-Advisor: Xavier Gomez-Mont. Email: gmont at cimat dot mx

SNI:

SNI - Level II. 2024 - Present.
SNI - Level I. 2014 - 2023.
Member of the National (Mexican) System of Researchers.

Undergraduate Academic Programs:

Undergraduate Academic Program "Licenciatura en Matemáticas para el Desarrollo" at the National School for Higher Eduaction ENES-Juriquilla, 2019
Committee member for the creation of the undergraduate program in Applied Mathematics at the Escuela Nacional de Estudios Superiores (ENES) in Juriquilla.

Grants:

5. Mathematical modelling and numerical analysis in fluid dynamics
Research project: DGAPA-PAPIIT-UNAM IN112222
Period: January 2022 - December 2024.

4. Modelling in blood flows and geophysical flows
Research project: DGAPA-PAPIIT-UNAM IN113019
 Period: January 2019 - December 2021.

3. Problemas inversos y directos en ecuaciones diferenciales parciales
Research project Conacyt-Sep A1-S-17634
Period: 2018 -  2021
 
2. Convective Instabilities and Hyperbolic Conservation Laws
Research project: DGAPA-PAPIIT-UNAM IA103015
Period: January 2017 - December 2018
 
1. Numerical analysis for hyperbolic conservation laws and geophysical flows
Research project: DGAPA-PAPIIT-UNAM IA104517
Period: January 2015 -  December 2016
 
Participation in other grants:
 
1. NSF Grant Collaborative Research: Global estimates of energy pathways and stirring by internal waves and vortical mode.
Period: 2021 - 2024
 

Current Students: 

Master thesis in progress:
 
1. David Peña Peralta
Master in Mathematics.
Universidad de Sonora.
Thesis: Modelo estocástico para propagación de aerosoles en la atmósfera
 

Posdocs:

3. Dra. Sarswati Shah. March 1, 2022 - 2024
Project: Two-layer shallow water flows with bottom topography
 
2. Dr. Nestor Abel Sánchez Goycochea. October 1, 2021 - September 30, 2022.
Project: Regularity problems in Geophysical models
 
1.  Velasco García, Ulises. February 2017 - February 2019
Project:  Numerical analysis and modelling in hyperbolic conservation laws and geophysical fluid dynamics

Graduated Students:

PhD Thesis:

1. César Rosales Alcantar. March 31 , 2023.
Posgrado en Ciencias Matemáticas.
Tí­tulo de tesis de Dcotorado: A new two-dimensional blood flow model with arbitrary cross sections & Generalized Quasi-geostrophy for moist spatially anisotropic atmospheric flows with phase change

Master Thesis:

1. José Alfonso Cabrera Sánchez. 
Graduate Program in Mathematics - UNAM
Thesis: Numerical analysis of liquid-gas flows in pipes
Fecha de graduación: Octubre 13, 2023

Undergraduate Thesis:

7. Guillermo Alberto Jimenez Frías. July 4, 2023
Undergraduate Program in Mathematics
University of Guanajuato
Tesis: A central-upwind scheme for the shallow water equations with density gradients.

6. David Peña Peralta. December 15 , 2022.
Undergraduate Program in Mathematics. 
University of Sonora.
Undergraduate thesis: Analysis of atmospheric instabilities through stochastic equations.

5. Brandon Alejandro Llaca Sánchez. January 17 , 2022.
Undergraduate Program in Applied Mathematics. 
Autonomous University of Queretaro
Undergraduate thesis : A kinetic numerical scheme for PDEs to model blood flows

4. Rodrigo Brito Interiano. September , 2021.
Undergraduate Program in Applied Physics and Advanced Technology, UNAM-Juriquilla 
Undergraduate thesis: "Método numérico central robusto para un modelo de flujo sanguíneo''.

3. Verónica Flores Mandujano. November 10, 2017.
State University of Queretaro. 
Undergraduate thesis: "Teoría de la parcela de fluidos para el estudio de inestabilidades atmosféricas y distribución de alturas de nubes''.

2. Olmo Guerrero Medina. June 16, 2017.
Multidisciplinary Unit for Teaching and Research - UNAM Juriquilla
Undergraduate thesis: "Exploración numérica sobre el impacto del exceso de núcleos de condensación en la cantidad de lluvia".

1. Claudia Guzmán Guzmán. December 14, 2018.
State University of Queretaro. 
Undergraduate thesis: "Teoría de Columnas de Fluido para el Desencadenamiento de Convección Atmosférica''.

Honors and Awards:

4. Youth Prize 2011 in the Academic Category Oct. 2011
Secretaria de la Juventud, Colima. Colima, Col.

3. Medal for best GPA (9.76/10) of the class of 2005. Nov. 2005
Univerisity of Guanajuato, Mexico

2. Medal for Academic Excellence Oct. 2000 “Ing. Arq. Rodolfo Chávez Carrillo” (GPA 10.0 / 10)
Univerisity of Colima, Mexico.

1. 2nd Place at National Contest, Mexican Mathematics Olympiad. Nov. 1999
Mexican Mathematical Society

Honors and Awards for Advised Students:

5. Teacher recognition - Universidad Privada del Norte - Perú.
September 28th, 2023.
Dr. Nestor A. Sánchez Goycochea has received this prize for his teaching performance. 
 
4. SIAM Award - Student Chapter UNAM. March 25, 2022.
The student César A. Rosales-Alcantar received an award in recognition of outstanding efforts and accomplishments on behalf of the SIAM Chapter at UNAM. Academic year 2021-2022. Awarded by the Society for Industrial and Applied Mathematics. Signed by the President Susanne C. Brenner and the Executive Director Suzanne L. Weekes. 
 
3. Award University of Sonora for the Student Academic Achievements. October 12, 2021 
The student David Peña Peralta from the University of Sonora received this award for his academic achievements as a student in the Undergraduate Program in Mathematics. David is working in his undergraduate thesis under my supervision.
 
2. Competition: Math Modelling Challenge. September 27, 2019
My student Cesar Rosales Alcantar participated in the competion "Math Modelling Challenge" organized by the Colombia and Mexico Sections of SIAM, where the topic was ``The Blue Economy''. The competition consisted of solving a problem using mathematics and modelling and the time limit was 10 hours. The event was presented by Gunter Pauli (author of``The Blue Economy'') from Japan. In total, 27 teams participated from 13 Universities from both countries. The winner team was in the graduate category was the Queretaro team. The team members were Ruth Corona, Elkinn Calderon, Eddel Ojeda and Cesar Rosales. More details at https://mexsiam.org/concursos .
 
1. Honorific mention in the Mixbaal award- Best undergraduate thesis in Applied Mathematics.  August 27, 2018
The student Olmo Guerrero Medina received an honorific mention at the Mixbaal award for the best thesis in Applied Mathematics. This awards is given by the Mexican Society for Scientific Computing and its Applications (SMCCA).
 

Publications and Preprints:

 
Edited books:
 
1. G- Hernandez-Duenas & M. A. Moreles. Mathematical and Computational Models of Flows and Waves in Geophysics. Springer (Book) (1), pp 1-195 (2022).
https://doi.org/10.1007/978-3-031-12007-7
 
Published Papers:
 
20. Global well-posedness of a model for precipitating convection with hydrostatic pressure under fast autoconversion and rain evaporation conditions. 
Temporary free access: https://authors.elsevier.com/c/1iUbN,WNxuZyK
Néstor A. Sánchez-Goycochea & G.- Hernandez-Dueñas.
Journal of Mathematical Analysis and Applications (2024)
Link to Journal
 
19. A patch in time saves nine: Methods for the identification of localised dynamical behaviour and lifespans of coherent structures. 
C. Blachut, C. González-Tokman & G.- Hernández-Dueñas.
Journal of Nonlinear Science (2023)
Link to Journal
 
18. A new two-dimensional blood flow model with arbitrary cross sections.
C.A. Rosales-Alcantar & G.- Hernández-Dueñas
ESAIM: Mathematical Modeling and Numerical Analysis (2023).
Link to Journal
 
17. Bathymetry and friction estimation from transient velocity data for one-dimensional shallow water flows in open channels with varying width.  
G. Hernandez-Duenas, M.A. Moreles  & P. Gonzalez-Casanova
Physics of Fluids (2023)
Link to Journal
 
14. Perturbations of the Landau Hamiltonian: Asymptotics of Eigenvalue Clusters.
G. Hernandez-Duenas, S. Pérez-Esteva, A. Uribe & C. Villegas-Blass
Ann. Henri Poincaré (2022).
https://doi.org/10.1007/s00023-021-01092-7
Link to Journal 
 
16. Impact of Wave-Vortical Interactions on Oceanic Submesoscale Lateral Dispersion. 
G. Hernandez-Duenas, M. Pascale Lelong, and Leslie M. Smith
The numerical model simulations upon which this study is based are too large to archive. The velocity and density data at 200 inertial periods as well as the data for the particles' trajectories from 200 to 210 inertial periods are available here.
Journal of Physical Oceanography (2021).
Link
 
15. A central-upwind scheme for two-layer shallow-water flows along channels with arbitrary geometry.
G. Hernandez-Duenas & J. Balbas
ESAIM: Mathematical Modeling and Numerical Analysis (2021).
Link
 
13. A well-balanced positivity-preserving central-upwind scheme for one-dimensional blood-flow models. 
G. Hernandez-Duenas, G. Ramirez-Santiago
International Journal for Numerical Methods in Fluids (2020). 
https://doi.org/10.1002/fld.4887
 Link to Journal
 
12. Weak- and Strong- Friction Limits of Parcel Models: Comparisons and Stochastic Convective Initiation Time.
G. Hernandez-Duenas, S. Stechmann and L. Smith.
Quarterly Journal of the Royal Meteorological Society (2019), Volume 145, No. 722, pp 2272-2291  (2019).
 Link to Journal
 
11. A positivity-preserving central-upwind scheme for isentropic two- phaseflows through deviated pipes.
G. Hernandez-Duenas, Ulises Velasco-García and Jorge Velasco Hernández. 
ESAIM: Mathematical Modelling and Numerical Analysis (2019).
 Link to Journal
 
10. A Hybrid Method to Solve Shallow Water Flows with Horizontal Density Gradients.
G. Hernandez-Duenas.
Journal of Scientific Computing (2017), Volume 73 (2-3) pp 753-782.
Link to Journal
 
9. A central-upwind scheme with artificial viscosity for shallow-water flows in channels.
G. Hernandez-Duenas and Abdelaziz Beljadid.
Advances in Water Resources 96 (2016) 323-338.
Link to Journal
 
8. Stability and Instability Criteria for Idelized Precipitating Hydrodynamics.
G. Hernandez-Duenas, Leslie M. Smith, and Samuel N. Stechmann.
Journal of Atmospheric Sciences, Vol 72, No. 6 (2015), pp. 2379-2393
Link to Journal
 
7. Algebras of semiclassical pseudodifferential operators associated with Zoll-type domains in cotangent bundles
G. Hernández-Dueñas and Alejandro Uribe.
Journal of Functional Analysis, 268 no. 7 (2015), pp. 1755-1807
Link to Journal

6. A Positivity Preserving Central Scheme for Shallow Water Flows in Channels with Wet-Dry States.
Jorge Balbás and G. Hernández-Dueñas. 
ESIAM: Mathematical Modelling and Numerical Analysis (M2AN) 48 (2014) 665-696.
Link to Journal
 
5. Investigation of Boussinesq dynamics using intermediate models based on wave-vortical interactions.
G. Hernandez-Duenas, Leslie M. Smith, and Samuel N. Stechmann
Journal of Fluid Mechanics, 747 (2014), 247-287
Link to Journal
 
4. Minimal models for precipitating turbulent convection
G. Hernandez-Duenas, Andrew J. Majda, Leslie M. Smith, and Samuel N. Stechmann.
Journal of Fluid Mechanics, 717 (2013), 576-611.
Link to Journal
 
3. Shallow Water Flows in Channels.
G. Hernández and Smadar Karni.
Journal of Scientific Computing 48 (2011), no. 1-3, 190-208.
Link to Journal
 
2. A Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann Invariants.
Smadar Karni and G. Hernández-Dueñas.
Journal of Scientific Computing, 45, (2010), 382-403.
 Link to Journal
 
1. A Hybrid Scheme for Flows in Porous Media.
Smadar Karni and G. Hernández-Dueñas.
Hyperbolic Problems: Theory, Numerics, Applications.
Proceedings of Simposia in Applied Mathematics, Volume 67, Part 2, (2009), 715-724.
Amer. Math. Soc., Providence, RI, (2009).
Link to Journal

Submitted papers:

  2. O. Guerrero-Medina & G. Hernandez-Dueñas. Exploring the excess of cloud condensation nuclei and rain suppression using a minimal 3D Boussinesq model with bulk cloud microphysics.
 
1. S. Shah & G.- Hernandez-Duenas. A weakly-compressible two-layer shallow water model in general channels.
 

Papers in preparation:

1. Jeffrey J. Early, Gerardo Hernández-Dueñas, Leslie M. Smith & M.-Pascale Lelong. Exact expressions for available potential energy and available potential vorticity.

Extended abstracts:

A Scheme for Shallow Water Flow with Area Variation.
Smadar Karni and G. Hernández-Dueñas.
American Institute of Physics.
AIP Conference Proceedings
International Conference on Numerical Analysis and Applied Mathematics
Rethymno, Crete, Greece, 18-22 September 2009. 1168 (2009), 1433-1436.
Link to Journal
 

Affiliations:

  • Sistema Nacional de Investigadores (SNI) - Level - I & II.              September 2013 - Present.

  • Sociedad Matemática Mexicana (SMM).                                                                 2017 - Present.

  • Sociedad Mexicana de Cómputo Científico y sus Aplicaciones (SMCCA).          2017 - Present.

  • Society for Industrial and Applied Math (SIAM).      Feb. 2010 - May 2011, Jan 2018-Present.

  • SIAM, Mexico Section (MexSIAM).                                                                        2018 - Present.

  • American Mathematical Society.            September 2005 - May 2011 , January 2019 - Present.

  • American Physical Society.                                                                                         2019-Present.

  • Registro Conacyt de Evaluadores Acreditados (RCEA).                       April 14, 2014 - Present.

  • Redes Temáticas Conacyt, Análisis y Ecuaciones Diferenciales.             June 2015 - June 2016. 

  • Redes Temáticas Conacyt, Modelación Matemática.                                June 2015 - June 2016.

  • American Metereologial Society.                                                                                    2019 -2020.

  • Royal Meteorological Society.                                                                         January 2019 - 2020.