Geometric and Homological Methods in the Representation Theory of Associative Algebras and Their Applications

Universidad de Antioquia, June 18-27, 2018, Medellín, Colombia

About this event

The topics of this school will be on geometric and homological methods in the representation theory of associative algebras, and their applications. This school will offer five short courses with an intensity of twelve hours each (six hours theoretical and six exercise hours). The lectures will run over the three following main topics:

  • Geometric aspects of the representation theory of algebras.
  • Homological aspects of the representation theory of algebras.
  • Applications of the representation theory of posets and algebras.

Objectives

Enhance the networking of researchers in the areas covered by the CIMPA school to facilitate students as well as professors from Colombia and from other countries in the region interested in geometric and homological aspects of the representation theory associative algebras and their applications, to motivate postgraduate studies in Mathematics in Colombia or abroad.

  • To enhance and increase the research groups in algebra in Colombia.
  • To establish links between researchers and students of the region.

Contact

cimpa2018medellin@udea.edu.co

Tourist guide

Important dates

Students: Deadline for registration and application to a CIMPA financial support: February 11, 2018.

Courses

Applications of the theory of representation of posets and algebras in cryptography
Agustin Moreno Cañadas, Universidad Nacional de Colombia, Colombia (amorenoca@unal.edu.co)

Abstract: In this course, we will studied applications of the theories of representation of quivers and posets in combinatorics, number theory, artificial intelligence and cryptography. In particular, it will be studied some aspects of the theory of homological persistence and its use in topological data analysis. Course material - here -
Slides: -1-, -2-, -3-, -4-, -5- .

Geometry of representations of algebras
Ryan Kinser, University of Iowa, United States (ryan-kinser@uiowa.edu)

Abstract: This short course will introduce participants to the geometry of representations of algebras, focusing on representation varieties of quivers (with relations). We will start with a concrete introduction to parametrizing representations with spaces of matrices satisfying certain conditions, and the corresponding bijection between orbits and isomorphism classes. This will include a brief recollection of relevant notions from algebraic geometry along the way. Next we will take an overview of the many connections between the representation theory of an algebra and the geometry of its representation varieties, covering for example the Artin-Voigt lemma, and various works of Bongartz, Riedtmann, and Zwara. In the last lecture, we will follow a line of inquiry initiated by Zelevinsky on the relation between orbit closures for Type A quivers and Schubert varieties.

Support theory for representations of groups and algebras
Henning Krause, Bielefeld University, Germany (henning.krause@math.uni-bielefeld.de)

Abstract:The notion of support provides a tool for classifying representations of groups and algebras. The course gives an introduction to this rich subject via the the study of triangulated categories with linear actions. The interplay between commutative and non- commutative algebra is an important ingredient, and small examples will be discussed in full detail.
Course material here https://www.math.uni-bielefeld.de/~hkrause/support.html

Special biserial and special multiserial algebras
Sibylle Schroll, University of Leicester, United Kingdom (schroll@leicester.ac.uk)

Abstract: Special biserial algebras are a well-studied class of tame algebras. They comprise many well-known fam- ilies of algebras such as gentle algebras, string algebras, and Brauer graph algebras. One of the reasons that their representation theory is so well understood is that their indecomposable representations are parametrised by so-called strings and bands. Special multiserial algebras, on the other hand, are mostly of wild representation type. So in particular, there is no hope to classify their indecomposable representations. However, we will see in this lecture course that many of the results known for special biserial algebras still hold for special multiserial algebras. In particular we will give an overview of the main results pertaining to special biserial algebras and we will introduce the class of special multiserial algebras.

Conference Speakers

NameAffiliationCountry
Sonia Trepode  Universidad Nacional de Mar del Plata Argentina
Vyacheslav Futorny   Universidade de Sao Paulo Brazil
Elizabeth Gasparim   Universidad Católica del Norte Chile
Erik Backelin   Universidad de los Andes Colombia
Milton Reyes   Universidad Nacional Colombia
Claude Cibils  Université de Montpellier France
Rachel Taillefer   - Slides - Université Blaise Pascal, Clermont- Ferrand II France
Dag Oskar Madsen  Nord University Norway
José A. Vélez- Marulanda   Valdosta State University United States
Ralph Schiffler   University of Connecticut United States
Marcelo Lanzilotta   Universidad de la República Uruguay

Posters

NameCountry
Cristian Arturo Chaparro Acosta   Argentina
Adriana Xavier Freitas   Brazil
Ana Melisa Paiba Amaya   Brazil
Heily Wagner   Brazil
Véronique Bazier-Matte   Canada
Aydee López Santana   Colombia
Geraldín Martínez, Juan Pablo Infante and Harrinson Arrubla Ramírez.  Colombia
Jarvin Jeffrey Gallego and Sebastian Marulanda  Colombia
Juan Manuel Hurtado Restrepo and Manuel Ricardo Orjuela   Colombia
Maria Camila Mejía García and María Del Rosario Valencia Arévalo   Colombia
Yesid Fernando Patiño Naranjo   Colombia

Committees

Scientific committee

NameAffiliationCountry
Claire Amiot Université Joseph Fourier, Grenoble France
Claude Cibils Université de Montpellier France
Henning Krause Bielefeld University Germany
Rachel Taillefer Université Blaise Pascal, Clermont- Ferrand II France
Sonia Trepode Universidad Nacional de Mar del Plata Argentina

Administrative and scientific coordinators

NameAffiliationEmail
Hernán Giraldo Universidad de Antioquia, Colombia hernan.giraldo@udea.edu.co
Dag Oskar Madsen Nord University, Norway dag.o.madsen@nord.no

Local organizing committee

NameAffiliationEmail
Verónica Cifuentes Universidad Distrital Francisco José de Caldas vcifuentesv@udistrital.edu.co
Ivón Dorado Universidad Nacional de Colombia iadoradoc@unal.edu.co
Eduardo do Nascimento Marcos Universidade de São Paulo enmarcos@gmail.com
Agustín Moreno Universidad Nacional de Colombia amorenoca@unal.edu.co
José A. Vélez Marulanda Valdosta State University javelezmarulanda@valdosta.edu

Logistic committee

NameAffiliationEmail
Faber Gómez (Coordinator) Universidad de Antioquia faber.gomez@udea.edu.co
Pedro Hernández Universidad de Antioquia pedro.hernandez@udea.edu.co
Yohny Calderón Universidad de Antioquia yfch03@gmail.com
Bilson Castro Universidad de Antioquia b9cast@gmail.com
Adriana Fonce Universidad de Antioquia amafeca@gmail.com
Andrés Franco Universidad de Antioquia andresfrancolondono@gmail.com
Yenny Molano Universidad de Antioquia yenny.molano@udea.edu.co
Ricardo Rueda Universidad de Antioquia ricardo.rueda@udea.edu.co

Participants

NameAffiliationCountry
Adriana Marcela Fonce C. Universidad de Antioquia Colombia
Adriana Marcela Fonce C.Universidad de AntioquiaColombia
Agustin Moreno Cañadas Universidad Nacional de Colombia Colombia
Jarvin Jeffrey Gallego Universidad Nacional de Colombia Colombia
Adriana Xavier Universidade Federal de Lavras. Brasil
Alejandra Suarez Galeano Universidad Distrital Colombia
Alex Sierra Universidade de São Paulo Brasil
Alexander Ramirez B. Universidad de Antioquia Colombia
Alexis Osorio Universidad de Antioquia Colombia
Ana Melisa Paiba Universidade de São Paulo Brasil
Andres Franco Universidad de Antioquia Colombia
Angie Yurani Puentes Universidad Distrital Colombia
Astrid Carolina Melo Universidad Nacional de Colombia Colombia
Beatriz de Rancell Montero Universidad de la Habana Cuba
Bilson Castro Universidad de Antioquia Colombia
Carlos Alejandro Espinal Molina Universidad de Antioquia Colombia
Carlos Zainea Universidad Nacional Colombia
Claude Cibils UNIVERSITE DE MONTPELLIER Francia
Claudio Rodriguez Beltran Universidad Nacional de Colombia Colombia
Cléber dos Santos Universidade Federal do Paraná Brasil
Cristian Arturo Chaparro Universidad de Buenos Aires Argentina
Cristian Felipe Gallego Universidad de Antioquia Colombia
Dag Oskar Madsen NORD UNIVERSITY Noruega
Daniel Jaramillo Universidad de Antioquia Colombia
Danna Moreno Universidad Nacional de Colombia Colombia
Diana Paola Franco Universidad de Antioquia Colombia
Diego Bravo Universidad de la República Uruguay
Diego Alejandro varelas Universidad de Antioquia Colombia
Diego Maca Universidad Nacional de Colombia Colombia
Dzoara Selene Nuñez Universidad Distrital Colombia
Edson R. Alvares U. Federal do Parana Brasil
Edward Salamanca Universidad Nacional de Cordoba Argentina
Elizabeth Gasparim U. CATOLICA DEL NORTE Chile
Erik Backelin Universidad de los Andes Colombia
Faber Gómez G. Universidad de Antioquia Colombia
Frederik Caneepel University of Antwerp Belgica
Gabriel Bravo Universidad Nacional de Colombia Colombia
Gabriele Bocca University of East Anglia. Reino Unido
Geraldin Martínez Universidad Nacional de Colombia Colombia
Gordana Todorov. NORTHEASTERN UNIVERSITY USA
Gregorio Rodriguez Universidad Nacional de Colombia Colombia
Guillaume Douville Université du Québec Canada
Harrinson Arrubla Universidad Nacional de ColombiaColombia
Heily Wagner Universidade Federal do Paraná Brasil
Hennning Krause Bielefeld University Alemania
Hernan Giraldo Universidad de Antioquia Colombia
Isaias Marin Universidad Nacional de Colombia Colombia
Ivon Dorado Universidad Nacional de Colombia Colombia
Jacob Andres Henao Universidad de Antioquia Colombia
Javier Andres Causil Universidad de Antioquia Colombia
Javier Coppola Instituto de Matématicas y Estadística Rafael Lagua Uruguay
Johny Calderon Universidad de Antioquia Colombia
Jorge H. Zea Universidad de Antioquia Colombia
Jorge Jimenez CIMPA España
Jose Alberto Velez Marulanda Valdosa State University USA
José Armando Vivero Universidad de la República Uruguay
José Suero Universidad Simon Bolivar Venezuela
Juan Camilo Sierra Universidad de Antioquia Colombia
Juan Diego Cifuentes Universidad Nacional de Colombia Colombia
Juan Esteban Lopez Universidad de Antioquia Colombia
Juan Hurtado R. Universidad Nacional de Colombia Colombia
Juan Pablo Infante Universidad Nacional de Colombia Colombia
Julia Pevtsova UNIVERSITY OF WASHINGTON USA
Julian Serna Universidad Nacional de Colombia Colombia
Karen Lizeth Martinez Acosta Universidade Federal de Minas Gerais Brasil
Kaveh Mousavand UNIVERSITE DU QUEBEC Canada
Lucas Queiroz Pinto Universidade Federal do Amazonas Brasil
Lucía Rossi Universidad Nacional de Mar del Plata Argentina
Makar Plakhotnyk Universidade de São Paulo Brasil
Manuel Orjuela Universidad Nacional de Colombia Colombia
Marcelo Lanzilotta Universidad de la República Uruguay
Maria Camila Mejía G. Universidad Nacional Colombia
Maria Valencia Areválo Universidad Nacional de Colombia Colombia
Armando Reyes Universidad Nacional Colombia
Noelia Bortolussi Universidad Nacional de Cordoba Argentina
Octavio Mendoza U. AUTONOMA DE MEXICO Mexico
Olmer Folleco S. Universidad Nacional de Colombia Colombia
Omar Saldarriaga Universidad de Antioquia Colombia
Oscar Daniel Bernal Miranda Universidad Distrital Colombia
Oscar Tujano Universidad Nacional de Colombia Colombia
Pedro Fernando Fernandez E. Universidad Nacional de Colombia Colombia
Pedro Hernandez Universidad de Antioquia Colombia
Rachel Taillefer UNIVERSITE CLERMONT AUVERGNE Francia
Ralf Schiffler UNIVERSITY OF CONNECTICUT USA
Raul Velasquez Universidad de Antioquia Colombia
Ryan Kinser UNIVERSITY OF IOWA USA
Santiago Duque Universidad de Antioquia Colombia
Sebastián Marulanda Universidad Nacional de Colombia Colombia
Sibylle Schroll UNIVERSITY OF LEICESTER United Kingdom
Sofia D'Alessio Instituto de Investigaciones Matemáticas, Luis A. Santalo Argentina
Sonia Trepode UNAL DE MAR DE PLATA Argentina
Veronica Cifuentes Universidad Nacional de Colombia Colombia
Véronique Bazier-Matte Université du Québec à Montréal Colombia
Vyacheslav Futorny Universidade de São Paulo Brasil
Wesley Dos Santos Universidade Federal do Paraná Brasil
Yenni Carolina Molano Universidad de Antioquia Colombia
Yesica Tatiana Carrasquilla Universidad de Antioquia Colombia
Yohny Calderon Universidad de Antioquia Colombia
Daniel Ricardo Barrero Universidad de los Andes Colombia
Carlos Ochoa Universidad Distrital Colombia
Maria Camila Ramirez Universidad Nacional Colombia
Carmen Beatriz Cuervo Arias Universidad del Tolima Colombia
Jairo Guasguita Ruiz UPTC Colombia
Jessica Gonzalez Universidad del Valle Colombia

Schedule

Week 1Monday 06/18Tuesday 06/19Wednesday 06/20Thursday 06/21Friday 06/22
9:00 - 10:00 SCHROLL KRAUSE SCHROLL KRAUSE CIBILS
10:00 - 10:30 INAUGURATION COFFEE COFFEE COFFEE COFFEE
10:30 - 11:30 VELEZ SCHROLL KRAUSE SCHROLL SCHROLL
11:30 - 12:00 COFFE COFFEE FREE AFTERNOON COFFEE COFFEE
12:00 - 13:00 KINSER KINSER KINSER KINSER
13:00 - 15:00 LUNCH LUNCH LUNCH LUNCH
15:00 - 16:00 TAILLEFER TAILLEFER MORENO TREPODE
16:00 - 16:30 COFFEE COFFEE COFFEE COFFEE
16:30 - 17:30 MADSEN FUTORNY MORENO MORENO
17:30 - 18:30 EXERCISES SESSION EXERCISES SESSION
Week 2 Monday 06/25 Tuesday 06/26 Wednesday 06/27
9:00 - 10:00 KRAUSE KRAUSE POSTER & LOUNGE TIME
10:00 - 10:30 COFFEE COFFEE
10:30 - 11:30 SCHIFFLER GASPARIM
11:30 - 12:00 COFFEE COFFEE FREE AFTERNOON
12:00 - 13:00 KINSER BACKELIN
13:00 - 15:00 LUNCH LUNCH
15:00 - 16:00 MORENO LANZILOTTA
16:00 - 16:30 COFFEE COFFEE
16:30 - 17:30 REYES MORENO
17:30 - 18:30 EXERCISES SESSION EXERCISES SESSION

Announcements and Financial Support

Announcements: (see) and Financial Support: (see)

Local and visa info

Registration Fees

There are no registration fees.


Lodging

We have reserved some of the facilities at the Maison Marie Poussepin (https://maisonmariepoussepin.com/) for the CIMPA School. The Maison Marie Poussepin is located in the town of Envigado, which is at the southeast of Medellin. Since all the academic activities are expected to take place here, it is strongly encouraged that all the participants make reservations at this place.

Here is the contact information about the Maison Marie Poussepin:

Professor Faber Gómez
faber.gomez@udea.edu.co

More info:
Phone: + (57) 4-480-53-70
Email: infomail.mmp@gmail.com
Address: Calle 37 Sur # 43a - 104 Envigado, Colombia


Travel and Directions

The easiest way of reaching Medellin from outside of Colombia is through the International Airport Jose Maria Cordoba (MED), which is located about 45 minutes away from Medellin. The recommended way of transportation from the airport to the Maison Marie Poussepin is through the airport white taxi services provided at the airport (about COL $ 75,000). There are also other available ways of transportation (see e.g. https://medellinguru.com/get-to-medellin-from-the-airport/).


Immigration and Customs statement

Although Colombia is a very welcoming country, there is a list of countries whose citizens are required to have a visa to enter our country (see http://www.colombia.travel/en/practical-information/visa or attached document page 11 -in spanish- ).

Is important to verify if your country is in the list of the countries (see page 17 in the attached document -in spanish- ) which for entering Colombia need the Yellow Fever Vaccine.

Please verify whether you require a Colombian visa or not. Upon arrival, foreign participants should ask for the PIP-6 stamp at the immigration stand, which identifies them as participants of a scientific event (as opposed to tourists). This is VERY IMPORTANT for the local organization.


About Medellin

Medellin is considered one of the most beautiful cities in South America. There are many interesting places and activities to visit and to enjoy. For more information about Medellin, please look at http://www.colombia.travel/en/where-to-go/andean/medellin.

Video and Photos

Organizing Institutions

Logo Universidad de Antioquia
Logo Universidad Nacional
Logo Universidad Distrital

Sponsors

Logo Colciencias
Logo IMU
Logo Icetex
Logo NORD

Logo Fundación UdeA
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