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.

Administrative and scientific coordinators

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

Important dates

TBA.

Contact

cimpa2018medellin@udea.edu.co

Tourist guide

Courses

Cluster-tilting theory in triangulated categories.
Claire Amiot, Université Joseph Fourier, Grenoble, (claire.amiot@ujf-grenoble.fr)

Abstract: In certain triangulated categories, quiver mutation appears as a combinatorial tool reflecting a natural operation called cluster-tilting mutation. This operation is the analogue of tilt in module or derived categories. In this course I will present basic notions on 2-Calabi-Yau triangulated categories, cluster-tilting objects and mutation, describe several class of examples, and compare the situation with the classical set up of derived categories with tilting objects.

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

Abstract: In this short course, we discuss how some techniques arising from the theory of representation of posets can be used in order to construct some visual cryptography schemes (VCS), systems of visual passwords (passdoodles) and CAPTCHAs. We also use the structure of the preprojective and preinjective components of some wild quivers in order to strenghthen some classical cryptographic systems.

Geometry of representations of algebras.
Ryan Kinser, University of Iowa, (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, (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, (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

NameAffiliationEmail
Claude Cibils Université de Montpellier Claude.Cibils@umontpellier.fr
Hernán Giraldo Universidad de Antioquia hernan.giraldo@udea.edu.co
Dag Oskar Madsen Nord University dag.o.madsen@nord.no
Eduardo do Nascimento Marcos Universidade de São Paulo enmarcos@gmail.com
Ralph Schiffler University of Connecticut schiffler@math.uconn.edu
Sonia Trepode Universidad Nacional de Mar del Plata strepode@gmail.com
José A. Vélez- Marulanda Valdosta State University javelezmarulanda@valdosta.edu

Committees

Scientific committee

NameAffiliationEmail
Claire Amiot Université Joseph Fourier, Grenoble claire.amiot@ujf-grenoble.fr
Claude Cibils Université de Montpellier Claude.Cibils@umontpellier.fr
Henning Krause Bielefeld University hkrause@math.uni-bielefeld.de
Rachel Taillefer Université Blaise Pascal, Clermont- Ferrand II rachel.taillefer@math.univ-bpclermont.fr
Sonia Trepode Universidad Nacional de Mar del Plata strepode@gmail.com

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

Organizing Institutions

Logo Universidad de Antioquia
Logo Universidad Nacional
Logo Universidad Distrital

Sponsors

Logo Colciencias
Logo IMU
Logo Icetex
Top