Escuela de Matemáticas
Universidad Nacional de Colombia Sede Medellín Calle 59A No 63 - 20 Medellín, Colombia phone: 57 (4) 4309000 Ext. 46313 email: jmramirez(at)unal.edu.co
Education
Post-Graduate ⋄ Richard S. Pierce post-doctoral fellow at The University of Arizona, Depart-ment of Mathematics. July 2007 - August 2009.
Graduate ⋄ Ph.D. in Mathematics, Oregon State University. Thesis title: Skew Brow-nian motion and branching processes applied to diffusion-advection in heterogenous media and fluid flow. Co-Advisors: Enrique Thomann and Edward Waymire. GPA: 4.0/4.0. July 2007.
⋄ M.Sc in Mathematics, Oregon State University. Master Paper: Monte Carlo
simulation of multiplicative cascades (application to two partial dif-ferential equations). Co-Advisors: Enrique Thomann and Edward Waymire. GPA: 4.0/4.0. 2002-2004.
Undergraduate ⋄ Civil Engineering with emphasis in Water Resources (degree equivalent to M.Sc.), Universidad Nacional de Colombia. Thesis title: Automated ex-traction of drainage networks from digital elevation models using the D8 model. Advisor: Jaime Velez. GPA: 4.3/5.0. 1996-2002.
⋄ Mathematics. Universidad de Antioquia. Medellin, Colombia. GPA: 4.7/5.0.
1997-2002. Short courses,
Workshops
⋄ Summer School in Geophysical Porous Media. Purdue University. West
Lafayette, IN. July 17 - 28, 2006.
⋄ Analytical and Stochastic Fluid Dynamics. Mathematical Sciences Research
Institute. Berkeley, CA. October 10 - 14, 2005.
⋄ IMA PI Summer Program for Graduate Students. Stochastic Partial
Differ-ential Equations and Environmental and Geophysical Modeling. University of Wyoming. Laramie, WYO. June 13 - July 1 2005.
⋄ Mathematical Modeling in Industry IX - A Workshop for Graduate Students.
Minnesota Center for Industrial Mathematics School of Mathematics Univer-sity of Minnesota. Minneapolis, MN. August 1-10, 2005.
⋄ Summer Graduate Program on Analysis of Algorithms. Mathematical Sciences
Research Institute. Berkeley, CA. June 1-18, 2004. 1
⋄ Probability and Partial Differential Equations in Modern Applied
Mathemat-ics. Institute for Mathematics and its Applications. Minnesota, MN. July 21-August 1, 2003.
⋄ XXIX Workshop in Stochastic Processes and their Applications, VII Brazilian
School on Probability. Angra dos Reis, Brazil. July 21 - August 3, 2003.
⋄ Summer Program in Real Analysis. Instituto Nacional de Matematica Pura e
Aplicada. Rio de Janeiro, Brazil. January 3 - February 23, 2001.
Employment
Post-doctoral Research⋄ Collaborative Research: Nonparametric Theory on Manifolds of
Shapes and Images, with Applications to Biology, Medical Imaging and Machine Vision. Senior Personnel. NSF Award No. DNS-0506011 to The University of Arizona and under the direction of Rabindra Bhattacharya - Mathematics, UofA. July 2008 - present.
⋄ Collaborative Research (CMG): Mathematical Theory and
Model-ing of Wave-Current Interactions. Project No. 2090GJC459 sponsored by the University of California and under the direction of Juan Restrepo -Mathematics, UofA. May 2008 - July 2008.
Graduate Research Assistantships
⋄ Dispersal of Invertebrate Communities in Stream Networks.
Con-structed and implemented a numerical model to study the effect of advective and diffusive dispersal of invertebrates on the stream network ecology. Results to be presented at the 5th International Conference on Ecological Informatics, Dec 2006, Santa Barbara, CA. Joint work with: J. Jones - Geosciences, S. Moore - Zoology, E. Waymire - Mathematics, OSU. August 2006 - present.
⋄ Fire History in Forests and Tree-age Distribution Data.
Conceptual-ized and implemented a stochastic model to estimate forest fire history records from scarce tree-age data. Compiled the results into a course module for a Geo-sciences IGERT graduate program. Joint work with: J. Jones - GeoGeo-sciences, F. Swanson - Forestry, E. Thomann , E. Waymire - Mathematics, OSU. May - August 2006.
⋄ Mathematical and Experimental Analysis of Transport Phenomena
in Highly Heterogeneous Porous Media. Obtained homogenization re-sults and modeled the random molecular motion for advective-diffusive trans-port in mediums with sharp heterogeneities. The results were published in SIAM Multiscale Modeling and Simulation Journal, 5(3)(2006). NSF Collabo-rations in Mathematical Geosciences Award DMS-0327705. PIs: E. Waymire, E. Thomann - Mathematics, B. Wood - Civil Engineering, R. Haggerty - Geo-sciences, OSU. September 2004 - May 2006.
⋄ Stochastic and Multiscale Structure Associated with the Navier
Stokes Equations. Developed and implemented numerical schemes to com-pute solutions to PDEs in Fourier space via random branching processes. The results were published in Journal of Computational Physics, 214 (2006). NSF Focus Research Group awards DMS-0073958 and DMS-0073865. PIs: R. Bhattacharya - Mathematics, U of Arizona, R. Guenther, M. Ossiander, E. Thomann and E. Waymire - Mathematics, OSU. May 2003 - September 2004. Undergraduate
Research Asssistanships
⋄ Exploratory Research of Sediment Transport in La Vieja River
Basin. Project contracted by Corporacion Autónoma Regional del Quindio to Posgrado en Aprovechamiento de Recursos Hidráulicos. Medellin, Colombia. December 2001 - August 2002.
⋄ General Inventory of Water and its Quality for Antioquia, phases I
and II. Project contracted by Centro de Ciencia y Tecnología de Antioquia y COLCIENCIAS to Posgrado en Aprovechamiento de Recursos Hidráulicos. Medellin, Colombia. March 2001 - August 2002.
⋄ Hydrologic Atlas of Colombia. Project contracted by Unidad de
Planeación Minero Energética to Posgrado en Aprovechamiento de Recursos Hidráulicos. Medellin, Colombia. March 2000 - March 2001.
Teaching ⋄ Graduate Mentor for an Eco-Informatics Summer Institute. Conducted lectures and advised undergraduate and graduate students in mathematics on research projects encompassing various mathematical applications to ecology. H.J. Andrews Experimental Forest, Oregon State University. Blue River, OR. June-August 2007.
⋄ Graduate Teaching Assistant. Conducted recitations and occasional lectures
in taught: algebra and trigonometry, vector calculus, probability and linear algebra. Department of Mathematics at Oregon State University. Cor-vallis, OR. September 2002 - May 2003 and September 2006 - May 2007.
⋄ Undergraduate Teaching Assistant. Conducted recitations in ordinary
dif-ferential equations. Department of Mathematics at Universidad Nacional de Colombia. Medellin, Colombia. January 2000 - March 2002.
Academic Awards
⋄ 2006-2007 William F. Burger Graduate Teaching Award. Presented by the Department of
Mathematics of Oregon State University. Corvallis, OR.
⋄ 2006-2007 Graduate Student Academic Achievement Award for academic excellence in
math-ematics. Presented by the Department of Mathematics of Oregon State University. Corvallis, OR.
⋄ 2003-2004 Graduate Student Academic Achievement Award for academic excellence in
math-ematics. Presented by the Department of Mathematics of Oregon State University. Corvallis, OR.
Scholarship and Creative Activity
Submitted ⋄ Multi-skew Brownian motion and diffusion in layered media. J. Ramirez. (2009)
Refereed journals
⋄ A Note on the Theoretical Foundations of Particle Tracking Methods
in Heterogeneous Porous Media. J. Ramirez, E. Thomann, E. Waymire, J. Chastanet, B. Wood. Water Resources Research, (2008)44, W01501,
⋄ A generalized Taylor-Aris formula and skew diffusion. J. Ramirez,
E. Thomann, E. Waymire, R. Haggerty, B. Wood. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 5(3)(2006), 786-801.
⋄ Multiplicative cascades applied to PDEs (two numerical examples).
J. Ramirez. Journal of Computational Physics, 214 (2006) 122-136.
⋄ Linking long-term water balances and statistical scaling to estimate
river flows along the drainage network of Colombia. G. Poveda, J. Vélez, O. Mesa, A. Cuartas, J. Barco, R. Mantilla, J. Mejía, C. Hoyos, J. Ramirez, L. Ceballos, M. Zuluaga, P. Arias, B. Botero, M. Montoya, J. Giraldo, and D. Quevedo. Journal of Hydrologic Engineering, 12(1)(2007), 4-13.
⋄ HidroSIG: an interactive digital atlas of Colombia’s
hydro-climatology. G. Poveda, O. Mesa, J. Vélez, R. Mantilla, J. Ramirez, O. Henandez, A. Borja, J. Urzola. Journal of Hydroinformatics, 9(2)(2007), 145-156.
⋄ HidroSIG Java: a tool for visualization and analysis of
hydroclimato-logical data (Spanish). J. Vélez, O. Mesa, G. Poveda, A. Borja, J. Ramirez, O. Hernandez, J. Urzola, P. Arias. Metereologia Colombiana, 6 (2002) 65-71.
⋄ Multiscaling of extreme values, detection of intermittency through
wavelets and evidence of deterministic chaos on wind dynamics over central Amazonia (Spanish). G. Poveda, C. Hoyos, J. Mejia, J. Ramirez. Metereologia Colombiana, 6 (2002) 21-32.
⋄ Strategies of automated drainage directions extraction from digital
elevation models (Spanish). J. Ramirez, J. Vélez. Avances en Recursos Hidraulicos, 9 (2002) 69-82.
⋄ A stochastic model of soil moisture dynamics under different
vegeta-tion covers in the coffee-producing region of Colombia (Spanish). G. Poveda, J. Ramirez., J. Jaramillo. Avances en Recursos Hidraulicos, 9 (2002) 47-56.
Invited talks ⋄ June 17, 2009. Modeling Wave Breaking and Its Dissipative Effects on Planetary-Scale Wave-Current Interactions. SIAM Conference on Mathematical and Computational Issues in the Geosciences. Leipzig, Germany.
⋄ April 26, 2008. Wave/Current Interactions and Wave Breaking.
Uncer-tainty Quantification Workshop. Department of Mathematics, The University of Arizona.
⋄ February 27, 2008. Probabilistic methods for diffusion in layered
me-dia. Mathematical Physics Seminar. Department of Mathematics, The Uni-versity of Arizona.
⋄ August 11, 2007. Probabilistic representations, majorizing kernels and
spectral behavior in fluid dynamics: Burgers equation. Applied Anal-ysis Seminar. Department of Mathematics, The University of Arizona.
⋄ June 8, 2007. Skew Brownian motion with multiple interfaces. Special
Ph.D. talk at Departmental Colloquium. Department of Mathematics, Oregon State University.
⋄ May 24, 2007. Multiple skew Brownian motion and applications.
Prob-ability Seminar, Department of Mathematics, Oregon State University.
⋄ April 6, 2007. Modelling time to extinction of ecological communities
in stream networks. Joint with Julia Jones (Geosciences, OSU). Applied Mathematics and Computation Seminar. Department of Mathematics, Oregon State University.
⋄ May 6, 2006. A mathematical model for forest fire history at the
stand level. Ecosystem Informatics First Annual Symposium, Oregon State University.
⋄ February 1, 2006. Skew Brownian motion and diffusion: a model for
heterogeneity. Probability Seminar, Department of Mathematics, Oregon State University.
⋄ January 8, 2006. Stochastic processes applied to partial differential
equations (Spanish). Graduate Seminar, Department of Mathemtics, Uni-versidad Nacional de Colombia sede Medellin.
⋄ February 11, 2005. Skew-diffusion and heterogeneous media I. Applied
Mathematics and Computation Seminar. Department of Mathematics, Oregon State University.
⋄ August 2, 2004. Modeling diffusion processes in heterogenous media.
Posters, Contributed talks
*speaker/presenter
⋄ December 2007. Markov Processes for Advection-Diffusion Transport
in Non-Smooth Media: Multi-Skew Brownian Motion and the Gen-eralized Taylor-Aris Formula. Poster presentation in 2007 American Geo-physics Union Annual Meeting. San Francisco, CA.
⋄ December 2006. Ecosystem informatics approaches to modeling
phy-sical processes and ecological communities in stream networks. Joint with J. Jones, T. Dietterich, X. Fern, M. Harmon and S. Moore*. 5th Inter-national Conference on Ecological Informatics. Santa Barbara, CA.
⋄ June 2006. A generalized Taylor-Aris formula and skew diffusion.
J. Ramirez, E. Thomann, E. Waymire*, R. Haggerty, B. Wood. Stochastic Processes in Mathematical Physics. Firenze, Italy.
⋄ March 2006. A generalized Taylor-Aris formula and skew diffusion.
J. Ramirez, E. Thomann, E. Waymire*, R. Haggerty, B. Wood. Conference on Stochastics in Science in honor of Ole E. Barndorff-Nielsen. Guanajuato, Mexico.
⋄ December 2005. A Generalized Taylor-Aris Formula and Skew
Diffu-sion. Poster presentation in 2005 American Geophysics Union Annual Meet-ing. San Francisco, CA.
⋄ July 2004. Monte Carlo modeling of PDEs via multiplicative cascades:
two examples. Poster presentation in 2004 annual SIAM meeting. Portland, OR.
⋄ August, 2003. A multiplicative cascade Monte Carlo solution to
li-near diffusion in Fourier domain. Poster presentation in IMA 2003 Sum-mer Program: probability and partial differential equations in modern applied mathematics. Minneapolis, MN.
⋄ July 2002. Scaling properties of extreme values, intermittence, and
Lyapunov exponents of wind and temperature dynamics in the cen-tral Amazonia. Joint with G. Poveda, J. Mejia, C. Hoyos. Contributed talk given at the International LBA Scientific Conference. Manuaus, Brazil.
⋄ July 2001. A hydro-climatological digital Atlas for Colombia. Joint
with J. Vélez, O. Mesa, G. Poveda, J. Barco, A. Cuartas, R. Mantilla, C. Hoyos, J. Mejía, B. Botero, C. Rios, D. Quevedo, J. Perez, J. Giraldo, L. Salazar, L. Ceballos, M. Zuluaga, P. Correa, and S. Vieira. Contributed talk for International Geographical Union Water study group in water sustainability. Zaragoza, Spain.
⋄ May 2001. A stochastic model of annual and inter-annual variability
of soil moisture in Colombia under different vegetation cover. Joint with G. Poveda*, J. Jaramillo. Poster presentation in 9th Latin-American Meteorology Congress. Buenos Aires, Argentina.