Higher Algebra and Representation theory

 Τhe research project HART is funded by the Hellenic Foundation for Research and Innovation (HFRI) under the "Basic Research Financing (Horizontal support for all Sciences), National Recovery and Resilience Plan (Greece 2.0)".

HART is a research project concerning the theory of derived and triangulated categories and their application to representation theory of finite dimensional algebras. 

Representation theory of finite dimensional algebras (and quivers) and derived categories have a long history of interaction with each other but also with other research areas in Mathematics. Various seminal works provide a strong link between the study of representations of an algebra with its derived category. This provided an ideal ground for developing both representation theory and triangulated categories as a unit but also in various divergent directions. The connection link between the latter two research areas is that derived categories and their triangulated structure turns out to be the right framework for studying several concrete problems in representation theory. On the other hand, such investigations gave tremendous ideas for developing further higher structures and higher invariants - entitled for short "Higher Algebra", for instance DG categories, Grothendieck derivators and infinity categories, in many different research areas. 

The objective of this project is to study  certain problems in representation theory using various techniques from "Higher Algebra". The proposed research will provide us with new knowledge on certain aspects of representation theory with a focus on the powerful methods from the rapidly growing research area of "Higher Algebra".  

Key Words: Derived and Triangulated Categories, DG Categories, Stable Derivators, Infinity Categories, Higher Categorical Enhancements, Representation Theory of Quivers, Auslander-Reiten Theory, Homological Dimensions (Finitistic Dimension, Dominant Dimension), Recollements of Abelian/Triangulated categories, Cleft Extensions, Realization Functors, Serre Duality, Cocompact Objects, Hochschild Cohomology, Singularity Categories, Cohen-Macaulay Modules.