A prevalent trend in the theory of operator algebras is the study of geometric/topological structures via bounded linear operators on a Hilbert space. The overarching idea is to associate a given geometric/topological structure with an operator algebra (usually a C*-algebra or von Neumann algebra), and use the rich structural theory of the latter to analyse the former (and vice versa). Examples of structures amenable to this kind of analysis include graphs and dynamical systems. Viewing such structures via an operator theoretic lens lies at the heart of my research.

Preprints

• J.A. Dessi and E.T.A. Kakariadis, Equivariant Nica-Pimsner quotients associated with strong compactly aligned product systems, preprint (104 pages).

Teaching

During my tenure as a student at Newcastle University, I have had the opportunity to engage with a variety of teaching activities. Find below a comprehensive summary.

CEG1716: Quantitative Geospatial Analysis Lecturer (September 2023 - October 2023)
CEG1716 is a Stage 1 undergraduate module for students studying Geographic Information Science and Geospatial Surveying and Mapping. The module is designed to equip students with the fundamental mathematics and statistics that they will need for their degree programme. I taught the first 5 weeks of this module, covering Trigonometry, Functions, Differentiation, Integration, Multivariable Calculus and Maclaurin/Taylor Series. I was responsible for delivering lectures and problem classes (5 hours per week), and for producing lecture notes and problem sheets. All assessment was electronic (and automatically marked) and I taught a cohort of 22 students.

MAS1606: Introductory Algebra Teaching Assistant (October 2022 - December 2022)
MAS1606 is a Stage 1 undergraduate module for students studying Mathematics/Statistics/Physics. The module covers the fundamentals of complex numbers, systems of linear equations, vectors and matrices. I worked as a teaching assistant for this module, running fortnightly tutorial sessions. There were 5 one-hour sessions, each being run 3 times (for 3 groups of students). Each student cohort consisted of 10-15 students. During the sessions, I guided the students through practice problems on the whiteboard and answered the students' questions.

A Level Further Mathematics Teaching Assistant (September 2017 - April 2023)
Newcastle University provides an A level Further Mathematics course for Sixth Form students whose schools do not offer this subject. I have been a teaching assistant on this course since its inception, my responsibilities being to mark work, invigilate mock exams and attend drop-in sessions to help the students with their homework. I also taught certain topics (e.g., vectors, proof by induction) when the course teachers were not available. The 2022-2023 variant of the programme was run as follows: every week the students attended a two hour lesson at Newcastle University. I supervised the first 15 minutes of these sessions while the students completed a short starter activity. I then collected the scripts and marked them whilst the students were being taught by the course teachers. At the end of the session, I returned the scripts to the students and offered feedback. The programme had a cohort of approximately 25 students (20 AS students and 5 A2 students).

Marking:

MAS3707/8707: Number Theory and Cryptography (February 2023 - May 2023)
I marked for the cryptography part of the module. The module had a cohort of 116 students and I marked 3 written assignments.

MAS2707: Vector Spaces, Groups and Algorithms (October 2022 - December 2022)
I marked for the linear algebra part of the module. The module had a cohort of 167 students and I marked 4 written assignments.

MAS1606: Introductory Algebra (October 2022 - December 2022)
The module had a cohort of 230 students and I marked 2 written assignments. Marking was split 50/50 between myself and another postgraduate.

MAS1702: Number Systems (March 2022)
The module had a cohort of 123 students and I marked 1 written assignment.

MAS3702/8702: Linear Analysis (October 2021 - December 2021)
The module had a cohort of 43 students and I marked 2 written assignments. Marking of the second assignment was split with the module leader.

MAS3712/8712: Matrix Analysis and Representation Theory (March 2021 - May 2021)
I marked for the representation theory part of the module. The module had a cohort of 46 students and I marked 2 written assignments.

Postgraduate Training

Operator Algebras and Groupoid C*-Algebras (February 2022 - July 2022)
I attended this course remotely via Zoom. The course, consisting of weekly lectures lasting 90 minutes each and focusing on C*-algebras and groupoids, was delivered by Dr Tristan Bice and Dr Karen Strung at the Institute of Mathematics of the Czech Academy of Sciences. For the course assessment, I delivered a 50 minute talk on my own research at an in-person workshop in Prague (see the Talks section for further details).

Algebras of Operators on Banach Spaces and Operator Ideals (October 2021 - January 2022)
I attended this course remotely via Zoom. The course, consisting of weekly lectures lasting 90 minutes each and focusing on Fredholm operators, Riesz operators and Schauder bases (among other topics), was delivered by Dr Bence Horváth and Dr Tommaso Russo at the Institute of Mathematics of the Czech Academy of Sciences. For the course assessment, I delivered a 50 minute talk on Johnson's Theorem (see the Talks section for further details).

Operator Algebras That One Can See II (March - June 2021)
I attended this course remotely via Zoom. The course, focusing on the interplay of C*-algebras and graphs, was delivered by Professor Piotr M. Hajac at the Mathematical Institute of the Polish Academy of Sciences. The course consisted of weekly lectures and recitation classes.

The 24th Internet Seminar on C*-Algebras and Dynamics (October 2020 - June 2021)
ISEM24 consisted of 3 phases: the lecture phase (October 2020 - February 2021), the project phase (March 2021 - May 2021) and the final workshop (June 2021). For the lecture phase, I read 13 sets of lecture notes covering the basics of C*-algebras and C*-dynamical systems. For the project phase, I worked with a small international group to prove that the free group on 2 generators is C*-simple. During the final workshop (which took place remotely), my group and I presented our work from the project phase. My slides can be found here, and the conference photo can be found here (see row 4, column 4 for me!).

Postgraduate Researcher Development Programme (September 2020 - September 2022)
This programme offered by Newcastle University serves to provide PhD students with transferable skills that are extraneous to their research. I attended various workshops in this programme during the first 2 years of my PhD studies.

Talks

University of Oxford Functional Analysis Seminar (April 2024)
Venue: University of Oxford
Talk title: Gauge-invariant ideal structure of C*-algebras associated with strong compactly aligned product systems, 60 minutes

Young Functional Analysts' Workshop 2024 (April 2024)
Venue: Newcastle University
Talk title: Gauge-invariant ideal structure of C*-algebras associated with strong compactly aligned product systems, 20 minutes

Newcastle University Analysis Seminar (November 2023)
Venue: Newcastle University
Talk title: Gauge-invariant ideal structure of C*-algebras associated with strong compactly aligned product systems, 60 minutes

Twinned Conference on C*-Algebras and Tensor Categories (November 2023)
Venue:  International Centre for  Mathematical Sciences
Talk title: Equivariant Nica-Pimsner quotients associated with strong compactly aligned product systems, 5 minutes

British Early Career Mathematicians' Colloquium (July 2023)
Venue: Birmingham University
Talk title: Gauge-invariant ideal structure of C*-algebras associated with strong compactly aligned product systems, 20 minutes

SAgE PGR Conference (January 2023)
Venue: Newcastle University
Talk title: Gauge-invariant ideal structure of C*-algebras associated with strong compactly aligned product systems, 15 minutes

Algebras of Operators on Banach Spaces and C*-Algebras Mini-workshop (July 2022)
Venue: Institute of Mathematics of the Czech Academy of Sciences
Talk title: Gauge-invariant ideal structure of C*-algebras associated with strong compactly aligned product systems, 50 minutes

Algebras of Operators on Banach Spaces and Operator Ideals Course (February 2022)
Venue: Remote
Talk title: Johnson's Theorem: An Introduction to Automatic Continuity Theory, 50 minutes

The 24th Internet Seminar on C*-Algebras and Dynamics Final Workshop (June 2021)
Venue: Remote
Talk title: The Reduced Group C*-Algebra of a Free Group and C*-Simplicity,  90 minutes
Note: I contributed to this talk as part of a group. I presented the first 9 slides (~12 minutes).

SAgE PGR Conference (July 2021)
Venue: Remote
Talk title: C*-Correspondences, Product Systems and their C*-Algebras, 15 minutes

Conferences, Seminars and Workshops

University of Oxford Functional Analysis Seminar (April 2024, University of Oxford)

Young Functional Analysts' Workshop 2024 (April 2024, Newcastle University. I was a member of the organising committee for this conference)

North British Functional Analysis Seminar (April 2024, Lancaster University)

Newcastle University Analysis Seminar (November 2023, Newcastle University)

Twinned Conference on C*-Algebras and Tensor Categories (November 2023, International Centre for Mathematical Sciences)

British Early Career Mathematicians' Colloquium (July 2023, Birmingham University)

Functional Analysis and Operator Algebras in Athens (March 2023, attended remotely)

SAgE PGR Conference (January 2023, Newcastle University)

Baby Steps Beyond the Horizon: Mathematics for Students (August 2022, attended remotely)

Algebras of Operators on Banach Spaces and C*-Algebras Mini-Workshop (July 2022, Institute of Mathematics of the Czech Academy of Sciences)

Aitken Lecture (June 2022, attended remotely)

Functional Analysis and Operator Algebras Seminar (February 2022, attended remotely)

The 9th Workshop on Operator Algebras and their Applications (February 2022, attended remotely)

Greek Mathematical Seminar (November 2021, attended remotely)

Baby Steps Beyond the Horizon: Mathematics for Students (September 2021, attended remotely)

Online Summer School on K-Theory and Representation Theory (July 2021, attended remotely)

SAgE PGR Conference (July 2021, attended remotely)

The 24th Internet Seminar on C*-Algebras and Dynamics Final Workshop (June 2021, attended remotely)

Functional Analysis and Operator Algebras Seminar (March 2021, attended remotely)

UK Virtual Operator Algebras Seminar (February 2021, attended remotely)

Hilbert C*-Modules Online Weekend (December 2020, attended remotely)

Ongoing Attendances:

• Newcastle University Analysis Seminar Series

• Newcastle University Algebra and Geometry Seminar Series

• North Atlantic Noncommutative Geometry Seminar Series

• North British Functional Analysis Seminar

Awards

I attained the following awards during my time as an undergraduate at Newcastle University.

• John Anderson Memorial Prize (2020): awarded for outstanding academic performance in the fourth year of my degree programme, ranking first among my cohort (final mark: 89/100).

• Barry Johnson Memorial Prize (2019): awarded for outstanding academic performance in the third year of my degree programme, ranking first among my cohort (final mark: 92.3/100).

• John Anderson Memorial Prize (2018): awarded for outstanding academic performance in the second year of my degree programme, ranking first among my cohort (final mark: 93.3/100).

• Endowed Prize (2017): awarded for outstanding academic performance in the first year of my degree programme, ranking second among my cohort (final mark: 87.5/100).

Other Interests