BrainMap

Simion-Sorin Breaz

- UNIVERSITATEA BABES BOLYAI

Teaching staff

Expertise & keywords

Categorical and combinatorial methods in representation theory Call name: Exploratory Research Projects - PCE-2012 call
PN-II-ID-PCE-2012-4-0100 2013 - 2016

Role in this project:

Coordinating institution: UNIVERSITATEA BABES BOLYAI

Project partners: UNIVERSITATEA BABES BOLYAI (RO)

Affiliation: UNIVERSITATEA BABES BOLYAI (RO)

Project website: http://algebra.math.ubbcluj.ro/~marcus/project-idei-2012-0100.html

Abstract:

In this this project we focus on group algebras of finite groups, path algebras of quivers, and their representations. We also investigate generalizations of these algebras, and actions of groups on them, leading to gradings and Galois coverings. The research in this field is very intense on an international level, being motivated by many important open problems, and it has multiple ramifications and applications. We combine the conceptualization provided by category theory with combinatorics. Our main directions of investigation are as follows: Clifford theory of blocks, Morita and derived equivalences graded by groups with order divisible by p; a categorical view on Brauer-Clifford groups; character correspondences vs. derived equivalences in connection with conjectures of Alperin, McKay, Dade, Isaacs, Navarro, Uno, Turull; reduction to simple or quasisimple groups of the calculation of numerical invariants associated to blocks; derived equivalences and tilting, and their graded versions; stable derived categories, n-angulated categories, exact categories, adjoint functors and separability; gradings and Galois coverings; combinatorial description of the basic algebra of a skew group algebra. In order to tackle these objectives we assemble a young team, and we also have in mind the formation of very young researchers.

Functors on Module Categories Call name: Projects for Young Research Teams - TE-2011 call
PN-II-RU-TE-2011-3-0065 2011 - 2014

Role in this project:

Coordinating institution: UNIVERSITATEA BABES BOLYAI

Project partners: UNIVERSITATEA BABES BOLYAI (RO)

Affiliation: UNIVERSITATEA BABES BOLYAI (RO)

Project website: http://math.ubbcluj.ro/~bodo/grant/TE_0065_eng.html

Abstract:

This project is focused on two sorts of objectives, as follows:

A) SCIENTIFIC OBJECTIVES:

The presumed research activity is developed on the following directions:

(I) FUNCTORS ON MODULE CATEGORIES:

(a) Commuting, respectively semi-commuting, properties (as those used for small and Mittag-Leffler modules) of functors defined on module categories or on other associated categories: quotient, stable or derived categories.

(b) Functors connecting module categories with other categories (e.g. connections with topological spaces via spectra).

(c) Equivalences and dualities between module categories (e.g. Morita and natural equivalences and dualities, Warfield dualities, Arnold-Fomin-Wickless duality).

(II) TORSION AND COTORSION THEORIES; PERPENDICULAR CLASSES.

(a) Torsion theories and kernels of functors (the interplay between the structure of an objects and properties of the kernel of some related functors);

(b) Cotorsion theories and cotorsion triples, approximations of modules and construction of adjoint functors;

(c) Closure properties for classes of static, adstatic or reflexive modules, Baer splitting properties, connections with the structure of projective modules.

B) ADMINISTRATIVE OBJECTIVES

1.Completion of the research infrastructure by assuring the bibliographical background (books, journals) and the material background of the research (computers, office consumables etc.)

2.Improving the level of knowledge of the team members and other young researchers and students.

FILE DESCRIPTION	DOCUMENT
List of research grants as project coordinator
List of research grants as partner team leader
List of research grants as project coordinator or partner team leader
Significant R&D projects for enterprises, as project manager
R&D activities in enterprises
Peer-review activity for international programs/projects