Joseph Dessi
Joseph's primary areas of interest are in C*-algebra and operator theory, as well as the theory of Hilbert C*-modules. His PhD research project focuses on investigating the structure of C*-algebras of product systems.
Project Title
'The Structure of C*-Algebras of Product Systems'
About
I am a PhD student in pure mathematics as well as a member of the Operator Theory and Operator Algebras research group at Newcastle University. I am primarily a functional analyst, but I am also interested in several topics from algebra (see the Research Interests section for more details).
Project Information
The project is a blend of functional analysis and algebra (with more of an inclination towards the former). Recent years have seen great strides in the theory of C*-algebras and operator algebras, particularly in their use for quantising geometrical structures. A notable breakthrough is the one-variable Gauge Invariant Uniqueness Theorem due to Katsura et al. The main goal of my project is to investigate multi-variable analogues of this theorem and explore its vast applications. I am particularly interested in applications pertaining to C*-dynamical systems and quantum mechanics.
Research Interests
I am interested in topics from both algebra and analysis. On the algebra side I am interested in commutative algebra, category theory and algebraic geometry. My MMath dissertation focused on these topics. On the analysis side I am interested in operator theory (and operator spaces/algebras/systems), the theory of C*-algebras (and its application to topics in applied mathematics such as quantum mechanics), the representation theory of C*-algebras and the theory of Hilbert C*-modules. My PhD project focuses primarily on these areas.
Education
Bachelor's degree: BSc (Hons) in Mathematics, Newcastle University, United Kingdom. I graduated in 2019 with first-class honours.
Master's degree: MMath (Hons) in Mathematics, Newcastle University, United Kingdom. I graduated in 2020 with first-class honours.
I completed my dissertation, entitled "Automorphism Group Schemes", under the supervision of Dr James Waldron. I also completed a funded summer project, entitled "Derivations of Commutative Algebras", at Newcastle University in 2018 again under the supervision of Dr James Waldron.
Supervisors
Contact
Email: j.dessi@newcastle.ac.uk