Hector E. Lomeli Education 1995
University of Minnesota. Minneapolis, MN. Ph.D., Mathematics. Adviser: Richard McGehee University of Minnesota. Minneapolis, MN. M.S., Mathematics. Universidad Autonoma Metropolitana. Mexico City, Mexico. B.A., Mathematics. Honors: Medal of Academic Merit., Member of the Academic Senate
1992 1989
Academic Positions August 2007- July 2008 August 1998- present August 2000- June 2001 August 1995- June 1998 June 1995- July 1995 Sep. 1989- June 1995 January 1989- June 1989
University of Texas. Dept. of Mathematics. Austin, TX Visiting Professor Instituto Tecnológico Autónomo de México. Dept. of Mathematics Associate Professor University of California. Mathematics Dept. Santa Cruz, CA Visiting Professor University of Colorado. Dept. of Applied Mathematics. Boulder, CO Postdoctoral Instructor University of Minnesota. Mathematics Department. Minneapolis, MN Summer Instructor University of Minnesota. Mathematics Department. Minneapolis, MN Teaching Assistant Universidad Autonoma Metropolitana. Mexico City, Mexico Undergraduate Teaching Assistant
Professional Experience Summer 1997
McKinsey and Co. Mexico City Office. Summer Associate
Research and Publications General Interests
Dynamical Systems, Billiards, Hamiltonian Mechanics, Chaotic Transport, Invariant manifolds, Melnikov's method, Heteroclinic Phenomena, and applications to Dynamic Programming, Finance and Economics.
Honors
Since July of 1999, member of SNI, the National Research System of Mexico. Promoted in 2005 to level 2.
Books
Lomeli, Hector and Rumbos, Beatriz. Métodos dinámicos en Economía. (2003). Thomson Learning. (Spanish)
Publications in refereed journals
1. Lomelí, Héctor, Rarimrez-Ros Rafaael and Meiss, James. Canonical Melnikov theory for diffeomorphisms (2008) Nonlinearity 21 485-508. 2. Lomelí, Héctor and García, César. Variations on a theorem of Korovkin. Amer. Math. Monthly 113 (2006), no. 8, 744--750.
3. Lomelí, Héctor and Calleja, Renato. Heteroclinic bifurcations and chaotic transport in the two-harmonic standard map. (2006) Chaos. 16, 023117. 4. Lomelí, Héctor E. Heteroclinic orbits and rotation sets for twist maps. Discrete Contin. Dyn. Syst. 14 (2006), no. 2, 343--354. 5. Lomelí, Héctor E. Symplectic homogeneous diffeomorphisms, Cremona maps and the jolt representation. Nonlinearity 18 (2005), no. 3, 1065-1071. 6. Lomelí, Héctor. Algunas aplicaciones de los números de Eisenstein. Miscelánea Mat. No. 38 (2003), 77-90. 7. Hector E. and Meiss, James. Heteroclinic intersections between invariant circles of volume-preserving maps. (2003) Nonlinearity 16 n.5. 1573--1595. 8. Lomelí, Héctor y Rumbos, B. La transformada de Laplace en economía. (2002) Gaceta de Economía 8, n. 15. 103-115. 9. Lomeli, Hector E. and Temzelides, Ted. Discrete Time Dynamics in a Random Matching Monetary Model. (2002) Econ. Theory 20 n. 2. 259270. 10. Lomelí, H. y Rumbos, B. Algunas interpretaciones económicas del factor de integración. Miscelánea Mat. No. 35 (2002), 65-75. 11. Lomeli, Hector E. and Meiss, James. Heteroclinic Orbits and Transport in a Perturbed, Integrable Standard Map. (2000) Phys. Lett. A 269 (5/6) 309-318. 12. Lomeli, Hector E. and Meiss, James. Heteroclinic Primary Intersections and Codimension one Melnikov Method for Volume Preserving Maps. (2000) Chaos 10 (1): 109-121. 13. Lenz, K.E., Lomeli, Hector E. and Meiss, James. Quadratic Volume Preserving Maps: an extension of a result of Moser. Regular and Chaotic Dynamics. 3 (1998) 122-131. 14. Lomeli, Hector E. and Meiss, James. Quadratic Volume Preserving Maps. Nonlinearity. 11 (1998) 557-574. 15. Lomeli, Hector E. Applications of the Melnikov Method to Twist Maps in Higher Dimensions. Erg. Th. and Dyn. Sys (1997) 16. Lomeli, Hector E. Transversal Heteroclinic Orbits for Perturbed Billiards. Physica D (1996) 59-80. 17. Lomeli, Hector E. Saddle Connections and Heteroclinic Orbits for Standard Maps. Nonlinearity 9 (1996) 649-668. Submitted
Lomeli, Hector and Ramirez-Ros Rafael. Separatrix splitting in 3D volumepreserving maps.
In preparation
Lomeli, Hector and Meiss, James. Chaotic transport formula in higher dimension
Other publications
Lomeli, Hector E. et. al. A mathematical model for an oxygen sensor. Inst. of math. and its appl. (1996). IMA preprint Series # 1422 Lomeli, H. et. al. Mathematical modeling of electronic rectifiers. Inst. of math. and its appl. (1996). IMA preprint Series # 1422
Conference Presentations / Seminar Talks February 2008 November 2007 September 2007 May 2007 November 2006 September 2006 June 2006 May 2006 March 2006 August 2005 June 2005 June 2005 May 2005 Diciembre 2004 October 2004 June 2004 May 2004 October 2003 April 2003 March 2003 October 2002 May 2002 October 2001 May 2001 April 2001 August 2000 July 2000 April 2000 March 2000 Februaryo 2000 October 1999 October 1999 August 1999 July 1999 May 1999 April 1999 March 1999 December 1998
University of Colorado. Dynamical Systems Seminar. Boulder, CO. University of Texas. Plasma Physics Seminar. Austin, TX University of Texas. Dynamical Systems Seminar. Austin, TX University of Texas. Dynamical Systems Seminar. Austin, TX IX Symposium on probability and stochastic processes. CIMAT. Guanajuato, México. First Joint meeting Canadian and Mexican Math. Societies. CIMAT. Guanajuato, México. Sixth International Conference on Dyn. Systems, Diff. Equations and Applications. AIMS. Poitiers, France. University of Texas. Dynamical Systems Seminar. Austin, TX Congreso de Actuaría y Matemáticas. UDLA. Puebla , México Seminar. Centro de Ciencias Físicas, UNAM. Cuernavaca, México Seminar. Area de Ecuaciones diferenciales y geometría. Universidad Autónoma Metropolitana Iztapalapa. México D.F. Colegio de Bachilleres XVI Science week México, DF. Seminar. Centro de Investigación en Matemáticas (CIMA). Universidad Autónoma del Estado de Hidalgo. Pachuca, Hidalgo First Colloquium of Dynamical Systems, Control and Applications. UAM-Casa de la primera imprenta. México, DF. XXXVII Conference of the Mexican Math. Society. Ensenada, Mexico AIMS Fifth International conference on Dynamical Systems and Differential Equations. Pomona, CA VI Joint AMS-SMM International Meeting. Houston, TX XXXVI Conference of the Mexican Math. Society. Pachuca, Mexico ITAM. Applied Math Seminar. Mexico City, Mexico UAM. Dynamical Systems Seminar. Mexico City, Mexico University of Colorado. Dynamical Systems Seminar. Boulder, CO. CB 14. XIII Science and research week. Mexico City, Mexico Midwest Dynamical Systems Conference. Boulder, CO Sixth SIAM Conference on Applications of D.S. Snowbird, UT IV International Symposium on Hamiltonian Systems and Celestial Mechanics. Guanajuato, Mexico ITAM. Applied Math Week. Mexico City, Mexico University of California. Applied Math Seminar. Santa Cruz, CA. Universidad Autónoma de San Luis Potosí. IV Encuentro Nacional de Sistemas Dinámicos. San Luis Potosí, México Georgia Inst. of Tech. Dynamical Systems Seminar. Atlanta, GA CalTech. Dynamical Systems Seminar. Pasadena, CA Midwest Dynamical Systems Conference. Evanston, IL UAM. VIII Math Week. Mexico City, Mexico ITAM. Applied Math Seminar. Mexico City, Mexico Universitat Politecnica de Catalunya. Barcelona, Spain IV Joint Meeting, AMS-SMM. Denton, TX University of Colorado. Dyn. Systems Seminar. Boulder, CO. UAM. Dynamical Systems Seminar. Mexico City, Mexico III International Symposium on Hamiltonian Systems and Celestial Mechanics. Patzcuaro, Mexico
September 1998 March 1998 November 1997 September 1997 April 1997 April 1997 June 1996 May 1996 March 1996 November 1995 October 1995 March 1995 January 1993
UNAM. Applied Math Inst. Colloquium. Mexico city, Mexico City University of New York. Math Seminar. New York, NY University of Colorado. Applied Math Seminar. Boulder, CO. Midwest Dynamical Systems Conference. Minneapolis, MN. U. of Co. Talk for the SIAM undergraduate chapter Boulder, CO. Southwest Dynamical Systems Conference. Denton, TX. Instituto Superior Tecnico. Lisbon, Portugal Universitat Politecnica de Catalunya. Barcelona, Spain Southwest Dynamical Systems Conference. Tucson, AZ. University of Colorado. Applied Math Seminar. Boulder, CO. University of Colorado. Applied Math Colloquium. Boulder, CO. Midwest Dynamical Systems Conference. Minneapolis, MN. AMS. Annual Joint Meeting. San Antonio, TX.
Advisees (undergraduate theses at ITAM, Mexico) May 2006 December 2005 November 2004 October 2004
July 2004
June 2002
June 2002
January 2002
Jesús Adalberto Calderón Güemez. La distancia al incumplimiento como medida de riesgo crediticio. Undergraduate thesis. (Spanish) Lorena Becerril Mirnada. Teoría de juegos evolutiva y dinámica de las votaciones. Undergraduate thesis. (Spanish) Alfonso Ignacio Viggers San Mamés. Periodicidad de funciones y el teorema de Sarkovskii. Undergraduate thesis. (Spanish) Cibeles García Hernández. Ecuaciones diferenciales estocásticas, procesos de difusión y fórmula de Feynman-Kac. Undergraduate thesis. (Spanish) Renato Calleja Castillo. Dinámica simpléctica y aproximaciones numéricas de separatrices y transporte caótico. Undergraduate thesis. (Spanish) Edgar Palomas Molina. Evidencia e implicaciones del fenómeno de Hurst en el mercado de capitales. Undergraduate thesis. (Spanish) (Winner of the IMEF prize 2002, Best thesis in Economics.) Yasmín Ríos Solís. Programación Dinámica y Activos Contingentes Aplicados a Dos Casos de Opciones Reales. Undergraduate thesis. (Spanish) Carlos Hernández. Bases ortonormales de soporte compacto para L2(R). Casos prácticos y aplicaciones. Undergraduate thesis. (Spanish)
Curriculum Vitae updated March of 2008
