FunSilting · Functorial techniques in silting theory
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2019-01-01 → 2021-03-31
- EU contribution
- €168,277
- Participants
- 1
- Scheme
- MSCA-IF-EF-ST
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Results in brief
Functorial techniques in silting theory
The setting of the project is an area of pure mathematics known as representation theory, which can be thought as the abstract theory of symmetry. The development of representation theory in the twentieth century has led to a beautiful theoretical framework, yielding interactions with other areas of mathematics such as geometry, combinatorics and topology. As well as being pervasive within mathematics, representation theory has various applications to real-world problems including to theoretical physics and data analysis. The central research objective of the project was to bring together two different approaches to representation theory. The first approach, using functorial techniques, comes from mathematical logic, which is an mathematical discipline where mathematical questions are encoded into formal statements that are manipulated according to a fixed algorithm. The second approach, silting theory, comes from abstract algebra, which is the traditional setting of representation theory. By taking advantage of the synergy between these two approaches, the project aimed to make fundamental advances in the field of silting theory. As well as these research objectives, the project aimed to provide the researcher with many opportunities to develop her management, teaching and communication skills.
Data: CORDIS, © European Union
Project objective
This project aims to develop topics in contemporary representation theory by making novel connections between two different approaches: tilting theory and model theory. Tilting theory is a set of tools that allows us to formally compare derived categories and has applications in many areas such as Lie theory, algebraic geometry and topology. Our work will take place in the richer setting of silting theory, which encompasses traditional tilting theory but also enables the study of important abelian subcategories of the derived category that are not necessarily derived equivalent to the ring. We will approach silting theory using techniques originating in mathematical logic, that is, we will use the model theoretic approach to purity. It has been observed for many years that there is a connection between purity and tilting theory but the underlying reasons for the link have still not been properly explained. Our new perspective aims to explain and deepen these connections. The key techniques we will use involve localisations of functor categories and their connection to a topological space called the Ziegler spectrum.There are two main objectives in this proposal: firstly we will strengthen the foundations of the connection between silting theory and purity and secondly we will apply our new approach to classification problems in the representation theory of finite-dimensional algebras.The Experienced Researcher (Dr. Rosanna Laking) will work on the project under the supervision of Prof. Angeleri Hügel at the University of Verona for a period of 24 months. In addition to the valuable exchange of knowledge between the Experienced Researcher and the large number of experts on tilting theory in the region of Verona, this fellowship will enable Dr. Laking to develop skills in teaching, project management and communication.
Original text from CORDIS.
Participants
- UNIVERSITA DEGLI STUDI DI VERONA · VeronaCoordinatorItaly
Links
Data: CORDIS, © European Union