CIMPA RESEARCH SCHOOL

Transcripción

1 Algebraic Structures, their representation and applications in geometry and non-associative models Research School CIMPA-UNESCO-MESR-MICINN-COLOMBIA CIMPA RESEARCH SCHOOL Algebraic Structures, their representation and applications in geometry and nonassociative models March 4 16 de 2012 Hotel Cartagena Plaza, Cartagena de Indias, Colombia ORGANIZERS UNIVERSIDAD DE ANTIOQUIA (U de A) UNIVERSIDAD NACIONAL DE COLOMBIA, SEDE MEDELLÍN (Unalmed) SPONSORS International Center for Pure and Applied Mathematics (CIMPA), Instituto Colombiano para el Desarrollo de la Ciencia y la Tecnología (COLCIENCIAS), Instituto Colombiano de Crédito Educativo y Estudios en el Exterior (ICETEX), Universidad de Medellín (U de M), Universidad de los Andes, Universidad EAFIT, Instituto Tecnológico Metropolitano (ITM), International Mathemathical Union (IMU), Universidad del Valle, Universidad del Norte, Universidad de Cartagena, Sociedad Colombiana de Matemáticas (SCM), Asociación Colombiana de Ciencias Exactas Físicas y Naturales (ACCEFYN)

2 Algebraic Structures, their representation and applications in geometry and nonassociative models Research School CIMPA-UNESCO-MESR-MICINN-COLOMBIA REPORT CIMPA RESEARCH SCHOOL Algebraic Structures, their representation and applications in geometry and nonassociative models March 4-16 de 2012 Hotel Cartagena Plaza, Cartagena de Indias, Colombia The International Center for Pure and Applied Mathematics (CIMPA), in order to promote the development of mathematical research in developing countries, promotes the organization of research schools with the primary objective of bringing together regional researchers and students with an interest in mathematics and its applications. Thus, in 2010, after a convocatory, the Institute of Mathematics, University of Antioquia (U de A) and the School of Mathematics, National University of Colombia, Medellín (Unalmed) organized a CIMPA Research School "Algebraic Structures, Their representation and Applications in geometry and non-associative models" (CIMPA-UNESCO- MESR-MICINN-COLOMBIA) which was held at the Hotel Cartagena Plaza during 4-16 March 2012 in the city of Cartagena de Indias, Colombia. The CIMPA Research School developed mainly in the following topics: Nonassociative Algebras Algebraic Geometry Representation Theory

3 AIM OF THE SCHOOL To establish links between international and national researchers and students. To promote the development of the subject through academic exchange among South American researchers. To update the knowledge of our local mathematical community by inviting senior local and international researchers. To introduce graduate and advanced undergraduate students to the current research topics. To enhance the Algebra community in Colombia. To facilitate students connect with international researchers who help them to get funding or at least acceptance for further studies abroad. To facilitate Colombian students and professors interested nonassociative algebras, representations and applications in geometry, study a Masters or a Doctoral degree in Colombia or abroad. SCIENTIFIC COMMITTEE Nicolas Andruskiewitsch, Universidad Nacional de Cordoba, Argentina Leticia Brambila Paz, Centro de Investigación en Matemáticas, Mexico Pedro Luis Del Ángel, Centro de Investigación en Matemáticas, Mexico Eduardo do Nascimento Marcos, Universidade de Sao Paulo, Brazil Alberto Elduque, Universidad de Zaragoza, Spain Esther García, Universidad Rey Juan Carlos, Spain Dieter Happel, Chemnitz University of Technology, Germany Cesar Polcino, Universidade de Sao Paulo, Brazil Ivan Shestakov, Universidade de Sao Paulo, Brazil Sonia Trepode, Unversidad Nacional del Mar del Plata, Argentina Otmar Venjakob, Mathematisches Institut, Universität Heidelberg, Germany Wilson Zuñiga, Centro de Investigación y de Estudios Avanzados, Mexico ADMINISTRATIVE AND SCIENTIFIC COORDINATORS Maria Jose Souto (Universidade da Coruña, A Coruña, Spain) mariaj@udc.es Alberto Medina (Université de Montpellier II, Montpellier, France) medina@math.univ-montp2.fr Hernán Giraldo (U de A, Medellín, Colombia) heragis@matematicas.udea.edu.co

4 ORGANIZING COMMITTEE Hernán Giraldo (U de A) Faber Gómez (U de A) Raúl Velázquez (U de A) Mauricio Londoño (U de A) Luis Alberto Wills (Unalmed) ACADEMIC ACTIVITIES SHORT COURSES (7) Almost of them each had a duration of 8 hours. INTRODUCTION TO JORDAN SYSTEMS, CONNECTIONS WITH LIE ALGEBRAS, Miguel Gómez Lozano y Cristina Draper, Universidad de Málaga, Spain. LIE ALGEBRAS: KILLING-CARTAN CLASSIFICATION, Alberto Elduque, Universidad de Zaragoza, Spain. INTRODUCTION TO TILTING THEORY, María Julia Redondo, Universidad de Buenos Aires, Universidad Nacional del Sur, Argentina. REDUCTION IN REPRESENTATION OF ALGEBRAS, Raymundo Bautista, Universidad Nacional Autónoma de Mexico, Morelia, Mexico. EXTENSION ALGEBRAS, Dag Oskar Madsen, University of Nordland, Norway. INTRODUCTION TO LOCAL ZETA FUNCITIONS, Wilson Zúñiga, Centro de Investigación y de Estudios Avanzados, Mexico. p-adic NUMBERS AND THE HASSE PRINCIPLE, Otmar Venjakob, Mathematisches Institut, Universität Heidelberg, Germany. INTERNATIONAL SPEAKERS (17) Alejandro Tiraboschi, Universidad Nacional de Córdoba, Argentina María Andrea Gatica, Universidad Nacional del Sur, Argentina Claudia Chaio, Universidad Nacional de Mar del Plata, Argentina Dalia Arstentein, Universidad de la República, Uruguay Eduardo do Nascimento Marcos, Universidad de Sao Paulo, Brazil Edison Alberto Fernández Culma, Universidad Nacional de Córdoba, Argentina

5 Flavio Ulhoa Coelho, Universidad de Sao Paulo, Brazil Ivan Shestakov, Universidad de Sao Paulo, Brazil Jeanneth Galeano, CINVESTAV, Mexico Marcelo Lanzilotta, Universidad de la República, Uruguay Mariano Suarez-Alvarez, Universidad de Buenos Aires, Argentina Otmar Venjakob, Mathematisches Institut, Universität Heidelberg, Germany. Paula Andrea Cadavid, Universidad de Sao Paulo, Brazil Pedro Luis Del Ángel, Centro de Investigación en Matemáticas, Mexico Peter Schneider, Westfälische Wilhelms-Universität Münster, Germany Vyacheslav Futorny, Universidad de Sao Paulo, Brazil Yadira Valdivieso, Universidad Nacional del Mar del Plata, Argentina NATIONAL SPEAKERS (20) Agustín Moreno Cañadas, Universidad Nacional de Colombia, Bogotá Carlos Cadavid, Universidad EAFIT, Medellín Claudio Rodriguez, Universidad del Rosario, Bogotá Erik Backelin, Universidad de los Andes, Bogotá Jarod Alper, Universidad de los Andes, Bogotá Faber Gómez González, Universidad de Antioquia, Medellín Héctor Quiceno, ITM, Medellín Ivon Dorado, Universidad Nacional de Colombia, Bogotá Jaime Andres Angel, Universidad de los Andes, Bogotá John Jader Mira, Universidad Nacional de Colombia, Medellín Danny de Jesús Gómez, Universidad Nacional Colombia, Medellín Juan Diego Vélez, Universidad Nacional de Colombia, Medellín Luis Alberto Wills Toro, Universidad Nacional de Colombia, Medellín Mary Luz Rodiño, Universidad de Antioquia, Medellín Milton Armando Reyes, Universidad Nacional de Colombia, Bogotá Olga Salazar, Universidad Nacional de Colombia, Medellín Oswaldo Lezama, Universidad Nacional de Colombia, Bogotá Pablo Felipe Ardila, ITM, Medellín Primitivo Acosta-Humanez, Universidad del Norte, Barranquilla Raul Eduardo Velasquéz Ossa, Universidad de Antioquia, Medellín RESULTS OF THE MEETING The event was attended by 106 people, of which 44 were national and international speakers, 21 international students, 34 national students and other participants were professors Colombians. Some students made contacts with international researchers to obtain funding or acceptance in the doctoral or postdoctoral programs in their places of origin.

6 The Colombian and other mathematical communities in the neighboring countries interested in the topics of the school were educated and updated on the latest research results of great importance. Consolidation of national and interregional working groups. Mathematical interests of teachers and students involved were greatly encouraged. Latest trends in the research topics were made accessible to graduate students and advanced undergraduate students. Interaction of students attending the meeting with highly renowned researchers in the topics of the meeting. CONCLUSIONS The CIMPA Research School, Algebraic Structures, Their representation and Applications in geometry and non-associative models, became an arena for exchange of knowledge among participants. It was a great opportunity to update and position our programs at national and international stages, which magnifies the possibility of signing agreements that facilitate, among other activities, the movement of trainees of our programs (in all participating universities) to institutions of origin of visitors, and consolidated the interaction with institutions like the University of Sao Paulo, Universidad Nacional Autonoma de Mexico, Universidad Nacional de Córdoba, Universidad Nacional del Sur, University of the Republic, among others. The proposed topics were well received by students who attended the event and especially at the University of Antioquia. This allowed advanced semester students of the program to find ideas to write an attractive thesis. Additionally, the participation of students from the Universidad Nacional de Colombia at Medellín improved links between our and their researchers and students. The contacts made during the event will be vital for further progress and development in education, science and technology in the country. In addition it will strengthen next academic events, such as algebra ALTENCOA meeting held every two years in the country. Exposure to the research of national and international researchers and their latest contributions to the academic community will be of great benefit to the development and consolidation of the graduate programs of our universities and helps our graduates in their future doctoral and postdoctoral studies.

7 FINANCIAL REPORT INCOME * 1EUR=$2.350 Universidad de Antioquia (U de A) $ CIMPA* $ (15,32 keur) ICETEX $ IMU* $ (1,66 keur) Universidad de los ANDES $ Universidad Nacional de Colombia, sede Medellín $ Universidad Cartagena $ Universidad de Medellín (U de M) $ Universidad EAFIT $ Universidad del Valle $ Universidad del Norte $ Instituto Tecnológico Metropolitano $ ACCEFYN $ SCM $ COLCIENCIAS $ REGISTRATION FEE $ TOTAL INCOME* * 1EUR=$2.350 EXPENSES $ (67,35 keur) Professors and Students U de A $ Students Scholars and Guests to the School $ Logistics $ Students Scholars CIMPA $ Guests ICETEX and U of M $ Servicios de Extensión $ Other Guests $ TOTAL EXPENSES* $ (61,04 keur) DIFFERENCE* $ (6,31 keur)

8 LIST OF PARTICIPANTS Name Country University 1 Agustín Moreno Colombia Universidad Nacional de Colombia amorenoca@unal.edu.co Cañadas 2 Alberto Elduque Spain Universidad de Zaragoza elduque@unizar.es 3 Alejandro Arrieta Colombia Universidad de Cartagena unialcartagena@hotmail.com 4 Alejandro Sánchez Yali Colombia Universidad de Antioquia alejandro.yali@hotmail.com 5 Alejandro Simarra Brazil Instituto de Matemática Pura e Aplicada alsica@cimpa.br 6 Alejandro Tiraboschi Argentina Universidad Nacional de Córdoba tirabo@famaf.unc.edu.ar 7 Alexis Carrillo Colombia Universidad de Cartagena udcarrillo@hotmail.com 8 Aníbal Álvarez Colombia Universidad Nacional de Colombia, sede Medellín afalvarezp@unal.edu.co 9 Armando Reyes Colombia Universidad Nacional de Colombia, Bogotá maresyev@unal.edu.co 10 Carlos Andrés Molina Colombia Universidad de Cartagena andres90422@hotmail.com 11 Carlos Cadavid Colombia Universidad EAFIT ccadavid@eafit.edu.co 12 Carlos Molina Colombia Universidad de Cartagena andres90422@hotmail.com 13 Catalina Ossa Colombia Universidad Nacional de Colombia, sede Medellín ossa.catalina@gmail.com 14 Claude Cibils France CIMPA claude.cibils@gmail.com 15 Claudia Chaio Argentina Universidad Nacional del Mar del Plata claudia.chaio@gmail.com 16 Claudio Rodríguez Colombia Universidad del Rosario crodriguezbe@unal.edu.co 17 Cristina Draper Spain Universidad de Málaga CDF@uma.es 18 Dag Oskar Madsen Norway University of Nordland Dag.Oskar.Madsen@uin.no

9 19 Dalia Arstentein Uruguay Universidad de la República 20 Daniel Andrés Lozoya Mexico Universidad Autónoma de San Luis Potosí Ponce 21 Daniel Lopez Aguayo Mexico Universidad Nacional Autónoma de México 22 Danny de Jesús Colombia Universidad Nacional de Colombia, sede Medellín Gómez 23 Eder Martelo Colombia Universidad de Cartagena 24 Edison Alberto Argentina Universidad Nacional de Córdoba Fernández Culma 25 Eduardo Marcos do Brazil Universidade de São Paulo Nascimento 26 Erick Backelin Colombia Universidad de los Andes 27 Faber Gómez González Colombia Universidad de Antioquia 28 Flavio Ulhoa Coelho Brazil Universidade de São Paulo 29 George Malambo Colombia Universidad de Cartagena Acosta 30 German Alonso Benítez Brazil Universidad Federal do Paraná 31 Gloria Miyeth Restrepo Colombia Instituto Tecnológico Metropolitano 32 Griselda Carolina Mexico Universidad Autónoma de San Luis Potosí Franco 33 Guillermo Cervantes Colombia Universidad del Norte 34 Gustavo Mata Uruguay Universidad de la República

10 35 Harry Smith Guzmán Colombia Universidad Nacional de Colombia, sede Medellín Guzmán 36 Héctor Quiceno Colombia Instituto Tecnológico Metropolitano 37 Hernán Giraldo Colombia Universidad de Antioquia 38 Hipolito Treffinger Argentina Universidad Nacional de la Pampa 39 Holmes Alberto Colombia Universidad Nacional de Colombia, sede Medellín Chavarría 40 Iryna Kashuba Brazil Universidade de São Paulo 41 Ivan Shestakov Brazil Universidade de São Paulo 42 Ivon Dorado Colombia Universidad Nacional de Colombia 43 Jackeñin Chacón Colombia Universidad de Cartagena 44 Jaime Andrés Ángel Colombia Universidad de los Andes 45 Jairo López Colombia Universidad de Cartagena 46 Jarnish Beltrán Mejía Chile Universidad de Santiago de Chile 47 Jarod Alper Colombia Universidad de los Andes 48 Javier Gutiérrez Argentina Universidad Nacional del Córdoba 49 Jeanneth Galeano Mexico CINVESTAV 50 Jhon Alexander Colombia Universidad de Antioquia Ramírez 51 John Jader Mira Colombia Universidad Nacional de Colombia, sede Medellín 52 José J. Torres Colombia Universidad de Medellín 53 José Negrete Colombia Universidad de Cartagena

11 54 Juan Diego Vélez Colombia Universidad Nacional de Colombia, sede Medellín 55 Julio Muñoz Colombia Instituto Tecnológico Metropolitano 56 Leandro Orozco Colombia Universidad de Antioquia 57 Lisbet de Jesús Orozco Colombia Universidad de Cartagena Martínez 58 Luciana Torres Colombia Universidad de Cartagena 59 Lucrecia Juliana Argentina Universidad Nacional del Sur Román 60 Luis Alberto Wills Colombia Universidad Nacional de Colombia, sede Medellín 61 Luis Enrique Ramírez Brazil Universidade de São Paulo 62 Luis Felipe Duque Colombia Universidad Nacional de Colombia Álvarez 63 Luis Giraldo Colombia Universidad Nacional de Colombia 64 Marcelo Lanzilotta Uruguay Universidad de la República 65 María Andrea Gatica Argentina Universidad Nacional del Sur 66 María Angélica Colombia Universidad de Cartagena Simancas 67 Maria Izabel Ramalho Brazil Universidade de São Paulo 68 María Julia Redondo Argentina Universidad Nacional del Sur 69 Mariano Suarez Argentina Universidad de Buenos Aires Álvarez 70 Mary Luz Rodiño Colombia Universidad de Antioquia

12 71 Mauricio Londoño Colombia Universidad de Antioquia 72 Milton Armando Reyes Colombia Universidad Nacional de Colombia 73 Miguel Gómez Lozano Spain Universidad de Málaga 74 Nadina Elizabeth Rojas Argentina Universidad Nacional de Córdoba 75 Norberto Tabarez Colombia Universidad de Antioquia 76 Olga Salazar Colombia Universidad Nacional, sede Medellín 77 Olmer Folleco Solarte Brazil Universidade de São Paulo 78 Oscar Francisco Casas Colombia Universidad de los Andes Sánchez 79 Oswaldo Lezama Colombia Universidad Nacional de Colombia 80 Otmar Venjakov Germany Universität Heidelberg 81 Pablo Felipe Ardila Colombia Instituto Tecnológico Metropolitano 82 Pablo Zadunaski Argentina Universidad de Buenos Aires 83 Paula Andrea Cadavid Brazil Universidade de São Paulo 84 Pedro Luis del Ángel Mexico CIMAT 85 Pedro Ortega Colombia Universidad de Cartagena 86 Peter Schneider Germany Universität Münster 87 Primitivo Acosta- Colombia Universidad del Norte Humanez 88 Quimey Vivas Argentina Universidad de Buenos Aires 89 Rafael Galeano Colombia Universidad de Cartagena 90 Raúl Eduardo Colombia Universidad de Antioquia

13 Velásquez 91 Raymundo Bautista Mexico Universidad Nacional Autónoma de México 92 Robinson Alexander Colombia Universidad de Antioquia Higuita 93 Rosa delgado Colombia Universidad de Cartagena 94 Rosendo García Mexico Universidad Autónoma de San Luis Potosí Delgado 95 Sandra Gutiérrez Colombia Universidad de Cartagena 96 Santiago Pineda Colombia Universidad Nacional de Colombia, sede Medellín Montoya 97 Saulo Andrés Carmona Colombia Universidad de Antioquia Toro 98 Sebastián Álvarez Colombia Universidad de Antioquia 99 Sergio Nicolas Chouhy Argentina Universidad de Buenos Aires 100 Vyacheslav Futorny Brazil Universidade de São Paulo 101 Wilson Zuniga Mexico CINVESTAV 102 Wincy Guerra Polania Colombia Universidad Nacional de Colombia, sede Medellín 103 Yadira Caicedo Colombia Universidad del Valle 104 Yadira Valdivieso Argentina Universidad de Mar del Plata 105 Yohny C. Gómez Colombia Universidad del Valle 106 Yuliya Zelenyuk South Africa University of Witwatersrand