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.

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.

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

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 KRAUSE SCHROLL KRAUSE SCHROLL TAILEFFER
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 TAILEFFER MORENO MORENO MORENO
16:00 - 16:30 COFFEE COFFEE COFFEE COFFEE
16:30 - 17:30 MADSEN FUTORNY TREPODE
Week 2 Monday 06/25 Tuesday 06/26 Wednesday 06/27
9:00 - 10:00 KRAUSE GASPARIM POSTER & LOUNGE TIME
10:00 - 10:30 COFFEE COFFEE
10:30 - 11:30 SCHIFFLER BACKELIN
11:30 - 12:00 COFFEE COFFEE FREE AFTERNOON
12:00 - 13:00 KINSER LANZILOTTA
13:00 - 15:00 LUNCH LUNCH
15:00 - 16:00 MORENO MORENO
16:00 - 16:30 COFFEE COFFEE
16:30 - 17:30 REYES VELEZ

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.

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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