Rodrigo Jesús Hernández Gutiérrez

Rodrigo Jesús
Hernández Gutiérrez
Postal address:
UAM Iztapalapa
Depto. Matematicas, AT-228
Av. San Rafael Atlixco 186, Col. Vicentina
Iztapalapa, 09340, Ciudad de México
México
Born October 27, 1984
in Mexico city
e-mail: [email protected]
Tel: +52 55 58044600 ext 3343
Current affiliation:
Profesor Titular B de Tiempo Completo (Visiting Professor)
Universidad Autónoma Metropolitana, Iztapalapa
Education
2016
• Postdoc (Continuum Theory), Nipissing University. North Bay, Ontario, Canada.
Supervisor: Logan Hoehn
2015
• Postdoc (Set-Theoretic Topology), University of North Carolina at Charlotte.
Charlotte, North Carolina, USA.
Supervisor: Alan Dow
2014
• Postdoc (Set-Theoretic Topology), York University. Toronto, Ontario, Canada.
Supervisor: Paul Szeptycki
2013
• Ph.D. in Mathematics, Universidad Nacional Autonoma de Mexico; Morelia, Michoacán, Mexico.
Supervisors: Michael Hrušák, Angel Tamariz Mascarúa
Dissertation: Disconnectedness properties of hyperspaces, spaces of remote points and
countable dense homogeneous spaces
2009
• M.Sc. in Mathematics, Universidad Nacional Autonoma de Mexico; Mexico City,
Mexico.
Supervisors: Angel Tamariz Mascarúa
Thesis: Products of cac spaces: an application of Set Theory to Topology
Education (continued)
2007
• B.Sc. in Mathematics, Universidad Nacional Autonoma de Mexico; Mexico City,
Mexico.
Supervisor: Alejandro Illanes Mejı́a
Thesis: Dendrites
2003
• Technical degree in Digital Systems, Instituto Politecnico Nacional; Ecatepec de
Morelos, State of Mexico, Mexico.
Research
Researcher level 1 of the National System of Researchers (SNI) of the Mexican
Council of Science and Technology (CONACyT) from 2015 a 2017.
I consider myself a General Topologist. Some topics I have worked on are: compactifications, continua theory, hyperspaces and homogeneous spaces. I am deeply interested in applications of Set
Theory to Topology.
The following is my list of publications. The numbering corresponds to the order in which the
papers were submitted to journals, regardless of publication status.
Submitted and accepted
21
20
19
18
17
16
• A fixed-point-free map of a tree-like continuum induced by bounded valence
maps on trees, (joint with L.C. Hoehn) submitted
• Reversible filters, (joint with A. Dow) submitted
• Homogeneity degree of symmetric products, (joint with V. Martı́nez de la Vega),
submitted
• Far points and discretely generated spaces, (joint with A. Dow), submitted
• Rigidity of the second symmetric product of the pseudo-arc, (joint with I. Calderón and A. Illanes), submitted
• Uniform powers of compacta and the proximal game, (joint with P. Szeptycki)
accepted to Topology and its Applications
Published
15
14
13
• Some observations on filters with properties defined by open covers, (con P.
Szeptycki) Comment. Math. Univ. Carolin. 56, 3 (2015) 355–364.
• Wijsman hyperspaces of non-separable metric spaces, (joint with P. Szeptycki)
Fund. Math. 228 (2015), 63–79.
• Countable Dense Homogeneity and λ-sets, (joint with M. Hrušák and J. van Mill)
Fund. Math. 226 (2014) 157–172.
(continued)
12
11
10
09
08
07
06
05
04
03
02
01
• A Whitney Map onto the Long Arc, Questions Answers Gen. Topology 32, 1 (2014),
145–152.
• Remote Points and Discretely Generated Spaces, Matematicki Vesnik 67, 1 (2015),
39–51.
• Periodic Points and Transitivity on Dendrites, (joint with Acosta, Naghmouchi
and Oprocha) to be published in Ergodic Theory and Dynamical Systems, 08/03/2016
(http://dx.doi.org/10.1017/etds.2015.137)
• Countable Dense Homogeneity and the Double Arrow Space, Top. Applications
160, 10, (2013), 1123–1128.
• Non-meager P-filters are Countable Dense Homogeneous, (joint with M. Hrušák)
Colloq. Math. 130 (2013), 281–289.
• Spaces of Remote Points, (joint with A. Tamariz-Mascarúa and M. Hrušák) Top.
Applications 159, 13 (2012), 3002–3011.
• Uniqueness of Hyperspaces of Indecomposable Arc Continua, (joint with A.
Illanes and V. Martı́nez-de-la-Vega) Glasnik Mat. 49 (69), (2014), 421–433.
• Rigidity of Symmetric Products, (joint with V. Martı́nez-de-la-Vega) Top. Applications 160, 13 (2013), 1577–1587.
• Rigidity of Hyperspaces, (joint with A. Illanes and V. Martı́nez-de-la-Vega) Rocky M.
J. of Math. 45 (1), (2015), 213–236.
• Disconnectedness Properties of Hyperspaces, (joint with A. Tamariz-Mascarúa)
Comment. Math. Univ. Carolin. 52, 4 (2011), 569–591.
• Uniqueness of Hyperspaces for Peano Continua, (joint with A. Illanes and V.
Martı́nez-de-la-Vega) Rocky Mountain J. Math. 43, 5 (2013), 1583–1624.
• Dendrites and Symmetric Products, (joint with G. Acosta and V. Martı́nez-de-laVega) Glas. Mat., III. Ser. 44, No. 1 (2009), 195–210.
Other papers
2014
• Ángel Tamarı́z: un pilar de la Topologı́a en México, (joint with Yasser Fermán
Ortiz Castillo) special contribution for a special volume in the Boletı́n de la Sociedad
Matemática Mexicana dedicated to the History of General Topology in Mexico, to be
published
Teaching Experience
September 2016 to August 2017
January 2015 to December 2015
• Visiting Professor, Universidad Autónoma Metropolitana, Iztapalapa, Department of Mathematics. Mexico city.
• Part Time Lecturer, The University of North Carolina
at Charlotte, Department of Mathematics and Statistics.
Charlotte, North Carolina.
(continued)
August 2014 to January 2015
July 2013 to June 2014
February 2013 to July 2013
February 2013 to July 2013
August 2012 to July 2013
February 2008 to July 2012
February 2009 to July 2009
August 2005 to July 2011
• Lecturer, level A, Universidad Nacional Autonoma de
México, Acatlán campus, Departments of Actuary and Applied Mathematics. Naucalpan de Juarez, State of Mexico.
• Postdoctoral Visitor, York University, Faculty of Science
and Engineering. Toronto, Ontario.
• Lecturer, Universidad Autónoma del Estado de México,
Cuautitlán Izcalli campus. Cuautitlán Izcalli, State of Mexico.
• Lecturer, level A, Universidad Nacional Autonoma de
México, Acatlán campus, Department of Actuary. Naucalpan de Juarez, State of Mexico.
• Lecturer, level B, Universidad Nacional Autónoma de
México, School of Sciences, Department of Mathematics.
Mexico City.
• Lecturer, level A, Universidad Nacional Autónoma de
México, School of Sciences, Department of Mathematics.
Mexico City.
• Lecturer, level A, Universidad Nacional Autonoma de
México, Acatlán campus, Department of Actuary. Naucalpan de Juarez, State of Mexico.
• Teacher Assistant, Universidad Nacional Autónoma de
México, School of Sciences, Department of Mathematics.
Mexico City.
Courses taught
08/2016
08/2015
06/2015
01/2015
08/2014
08/2014
08/2014
09/2013
02/2013
02/2013
02/2013
08/2012
02/2011
08/2010
08/2010
02/2010
08/2009
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
19/2017
12/2015
08/2015
04/2015
11/2014
11/2014
11/2014
05/2014
07/2013
07/2013
07/2013
01/2013
07/2011
01/2011
01/2011
07/2010
01/2010
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Applied linear algebra, UAM Iztapalapa
College algebra, UNC Charlotte
College algebra, UNC Charlotte
Matrices and linear algebra, UNC Charlotte
Differential and integral calculus 1, UNAM Acatlán
College algebra 1, UNAM Acatlán
Discrete mathematics, UNAM Acatlán
Calculus for the life and social sciences, York University
Differential and integral calculus 3, UNAM Acatlán
Set theory 1, UNAM School of Sciences
Operations research, Cuautitlán Izcalli campus, UAEM
Sets and logic, UNAM School of Sciences
Set theory 1, UNAM School of Sciences
College algebra 2, UNAM School of Sciences
Set theory 1, UNAM School of Sciences
Set theory 2, UNAM School of Sciences
Set theory 1, UNAM School of Sciences
(continued)
08/2009
02/2009
08/2008
08/2008
02/2008
02/2008
–
–
–
–
–
–
01/2010
07/2009
01/2009
01/2009
07/2008
07/2008
•
•
•
•
•
•
08/2007
08/2007
02/2007
02/2007
08/2006
08/2006
02/2006
02/2006
08/2005
–
–
–
–
–
–
–
–
–
01/2008
01/2008
07/2007
07/2007
01/2007
01/2007
07/2006
07/2006
01/2006
•
•
•
•
•
•
•
•
•
Set theory 1 (TA), UNAM School of Sciences
Mathematical analysis 1, UNAM Acatlán
Topology 2 (TA), UNAM School of Sciences
Number theory 1 (TA), UNAM School of Sciences
Analytic geometry 1, UNAM School of Sciences
Topology seminar B (hyperspace theory, TA), UNAM School of Sciences
Topology 3 (TA), UNAM School of Sciences
Algebraic geometry 2 (TA), UNAM School of Sciences
Mathematical analysis 2 (TA), UNAM School of Sciences
Algebraic geometry 1 (TA), UNAM School of Sciences
Mathematical analysis 1 (TA), UNAM School of Sciences
Linear algebra 1 (TA), UNAM School of Sciences
Topology 1 (TA), UNAM School of Sciences
College algebra 2 (TA), UNAM School of Sciences
College algebra 1 (TA), UNAM School of Sciences
I must mention that TAs (Teacher Assitants) at the School of Sciences, UNAM are not only asked
to grade homework assignments and exams as it is usual in other parts of the world. It is also
a responsability of the TA to lecture twice a week for an hour about theory not covered by the
professor and exercises assigned.
Courses for Teachers taken
Summer 2009
• Plotting the Complex Plane, Universidad Nacional Autónoma de México,
School of Sciences, Department of Mathematics. Mexico city.
Revised theses
2016
2015
2014
2010
2009
• Uniqueness of the second and third symmetric product for meshed continua,
Luis Alberto Guerrero Méndez, Ph.D. in mathematics, Facultad de Ciencias Fı́sicoMatemáticas BUAP, Puebla.
• Infinitary combinatorics and Ramsey type theorems, Jareth Zuleyca Torres
Reyes, Mathematician, Facultad de Ciencias UNAM, Mexico City.
• The symmetric product of topological spaces, Irene Rosas Nuñez, Mathematician,
Facultad de Ciencias UNAM, Mexico City.
• From Lebesgue measure to large cardinal, Judith Campos Cordero, Mathematician, Facultad de Ciencias UNAM, Mexico City.
• Some properties of Mrówka-Isbell spaces, Noriko Amano Patiño, Mathematician,
Facultad de Ciencias UNAM, Mexico City.
Talks at Conferences
Invited talks
Mayo 2016
May 2015
March 2015
• Unique hyperspaces and homeomorphisms, Invited speaker, 13th Annual
Workshop on Topology and Dynamical Systems, North Bay, Ontario, Canada.
• Some problems in the theory of hyperspaces Semi-plenary speaker at the
2015 Spring Topology and Dynamical Systems Conference. Bowling Green, Ohio,
United States.
• The proximal game for topological spaces Topology Seminar at UNC
Greensboro. Greensboro, North Carolina, United States.
International Conferences
September 2016
Marzo 2016
August 2015
August 2014
August 2014
March 2014
March 2014
April 2012
March 2012
February 2012
July 2011
September 2010
• Spaces that are discretely generated at infinity, Workshop on Set
Theory and Its Applications in Topology. Casa Matemática Oaxaca. Oaxaca,
Mexico.
• Reversible filters, 50th Spring Topology and Dynamics Conference. Waco,
Texas, USA.
• Compactifications of discretely generated spaces, International Conference on Set-Theoretic Topology and its Applications. Yokohama, Kanagawa, Japan.
• Uniform powers of compacta and the proximal game, Mexican International Conference on Topology and its Applications. Cocoyoc, Morelos,
Mexico.
• Whitney maps with non-metrizable codomain, Mexican International
Conference on Topology and its Applications. Cocoyoc, Morelos, México.
• Whitney maps onto non-metrizable arcs, 2014 Spring Topology and
Dynamics Conference. Richmond, Virginia, USA.
• Wijsman hyperspaces of non-separable metric spaces, 2014 Spring
Topology and Dynamics Conference. Richmond, Virginia, USA.
• New Results on Countable Dense Homogeneity, 2012 Ibero-American
Conference on Topology and its Applications. Guanajuato, Guanajuato state, Mexico.
• Countable Dense Homogeneous Filters, 46th Spring Topology and Dynamics Conference. Mexico city, Mexico.
• Countable Dense Homogeneous Filters, Winter School on Abstract
Analysis - Section Set Theory and Set Theoretic-Topology. Hejnice, Czech
Republic.
• Classifying spaces of Remote Points for some Metrizable Spaces,
Prague Topological Symposium 2011. Prague, Czech Republic.
• Disconnectedness properties of hyperspaces, International Conference Japan-Mexico on Topology and its Applications. Colima, Colima state,
Mexico.
(continued)
June 2010
• The problem of unique hyperspaces for Peano continua, International Conference on Topology and its Applications. Nafpaktos, Greece.
National Meetings, Schools and Conferences in Mexico
November 2012
June 2012
November 2012
October 2010
October 2010
November 2009
November 2009
September 2009
Noviembre 2008
October 2008
April 2008
November 2007
• Countable Dense Homogeneous Spaces, National Meeting of the Mexican Mathematical Society. Querétaro, Querétaro state.
• Ways to arrange a countable dense set, Young Researchers Symposium.
Toluca, State of Mexico.
• About the hyperspace of subcontinua of a smooth fan, 7th Student’s
Workshop on Continua Theory and Hyperspaces. Puebla, Puebla state.
• Casicomponentes, Hiperespacios y Grupos, Student’s conference
“Aquelarre Matematico”. Mexico city.
• Remote Points, “Jornadas de topologı́a”. Puebla, Puebla state.
• Counting composants on indecomposable continua, 4th Students
Workshop on Continua Theory and Hyperspaces. Toluca, State of Mexico.
• Extreme disconnectedness properties in linearly ordered spaces
and hyperspaces, Conferences on the 70th anniversary of the School of
Science, UNAM. Mexico city.
• Boolean spaces, Seminar for Fellow Students, Institute of Mathematics,
UNAM. Mexico City.
• Souslins problem, Jornadas de Topologa. Pátzcuaro, Michoacán.
• Product of cac spaces, National Meeting of the Mexican Mathematical
Society. Valle de Bravo, State of Mexico.
• 45 Topological Characterizations of dendrites, Latinoamerican Meeting of Mathematics Students EXPRIME 2007. San Luis Potosı́, San Luis
Potosı́.
• Dendrites with unique symmetric products, Second Students Workshop on Continua Theory and Hyperspaces. Institute of Mathematics,
UNAM. Cuernavaca, Morelos.
Fellowships and Schollarships
2015
2013 to 2014
2011 to 2012
2006 to 2011
• CONACyT scholarship for posdoctoral research abroad.
• Visiting researcher at The Fields Institute for Research in Mathematical Sciences, University of Toronto during my postdoctoral position in York University.
• Fellow student at the Center of Mathematical Sciences (Morelia) during my
Ph.D. studies.
• Fellow student at the Institute of Mathematics (Mexico city) during my M.Sc.
and Ph.D. studies.
Fellowships and Schollarships (continued)
2002 to 2006
• Thanks to my medals in the Mexican Mathematics Olympiad, I was awarded
scholarships for my undergraduate studies by both the National Council of
Science and Technology (CONACyT) and the TELMEX foundation.
Memberships to Mathematics Societies
starting 2002
starting 2009
starting 2009
• Member of the Mexican Mathematical Society (SMM).
• Member of the AMS (US).
• Member of the MAA (US).
Languages
2005
2004
2002
from 1997 to 1999
•
•
•
•
Japanese language proficiency exam, level 3, 388 out of 400 points.
Japanese language proficiency exam, level 4, 393 out of 400 points.
Methodology Course for English Teachers, 100 hours.
Advanced courses of the English language in reading, writing, listening
and speaking.
Others
July 2002
November 2001
November 2000 and 2001
1999 to 2002
• Contestant in the 42nd International Mathematical Olympiad.
Glasgow, Scotland.
• Contestant in the 12th Mexican Physics Olympiad, obtained a Honorable Mention. Ensenada, Baja California, Mexico.
• Constestant in the 14th and 15th Mexican Mathematical Olympiad, obtained silver and gold medal, respectively.
• During high school, I participated in various academic competitions. In the “Interpolitécnicos” of the Instituto Politécnico Nacional, I scored first place among all contestants in four mathematics subjects and one physics subject. I also got distinctions
in the following competitions: “Andrei N. Kolmogorov Contest of
Mathematics” organized by Anahuac University in 2001, “Pierre
de Fermat Contest of Mathematics” organized by the Physics and
Mathematics School of the Instituto Politécnico Nacional in 2001
and “Tippens Contest of Physics” organized by McGrawHill publishing house in 2001. I obtained an honorable mention of the
“Bernardo Quintana Arrioja prize” in the “Academic Excellence”
category in 2002; this prize is awarded by the Instituto Politécnico
Nacional and the “Asociación de Apoyo a la Juventud”.