# Dr Evgenios Kakariadis

Lecturer in Pure Mathematics

- Email: evgenios.kakariadis@ncl.ac.uk
- Telephone: +44 (0) 191 208 5374
- Personal Website: https://sites.google.com/view/evgenioskakariadis
- Address: School of Mathematics, Statistics & Physics

Herschel Building,

Newcastle University

Newcastle upon Tyne

NE1 7RU

## Background

Dr Evgenios Kakariadis is a Lecturer in Pure Mathematics for the School of Mathematics, Statistics & Physics at Newcastle University. His area of expertise is operator algebras.

**Current roles:**

- Secretary of the North British Functional Analysis Seminars.
- Teaching Curriculum Coordinator for the Pure Mathematics Section.

#### Professional Appointments:

- 2014 - today: Lecturer in Pure Mathematics, School of Mathematics and Statistics, Newcastle University, UK.
- 2013 - 2014: Postdoctoral Fellow, Dept of Mathematics, Ben Gurion University, Israel. Supervisor: Orr M. Shalit.
- 2011 - 2013: Postdoctoral Fellow, Dept of Pure Mathematics, University of Waterloo, Canada. Supervisor: Kenneth R. Davidson.

#### Education:

- 2011: PhD in Mathematics, Dept of Mathematics, University of Athens, Greece. Advisor: Aristides Katavolos.

PhD Thesis:*Operator Spaces and Operator Algebras: Semicrossed Products of Operator Algebras*. - 2007: MSc in Pure Mathematics, Dept of Mathematics, University of Athens, Greece. Advisor: Marina Haralampidou.

MSc Thesis:*Wedderburn-type Structure Theorems in Topological Algebras*. - 2004: Ptychion in Mathematics, Dept of Mathematics, University of Athens, Greece.

#### Languages:

- English.
- French.
- Greek (native).

#### Databases:

**MathScinet:****SCOPUS:**Click here.**Google Scholar:**Click here.

## Teaching

#### 2019-2020:

**Semester 1:**MAS8754 Topics in Analysis.

#### Teaching Certificates:

**Fellow**of the Higher Education Academy (2017).**Newcastle Teaching Award**(2016).**Associate Fellow**of the Higher Education Academy (2015).

#### Recognition:

- Shortlisted for The Education Award in the
**Outstanding Contribution to Teaching - SAgE Faculty**category by the Students' Union (2018/19). - Shortlisted for The Education Award in the
**Outstanding Feedback** - Nominated for the Teaching Excellence Award in the
**Research Supervision**category by the Students' Union (2016/17). - Shortlisted for the Teaching Excellence Award in the
**Outstanding Feedback**category by the Students' Union (2014/15). - Shortlisted for the Teaching Excellence Award in the
**Outstanding Feedback**category by the Students' Union (2014/15).

#### Committees:

- School Business and Engagement Committee (2018/today).
- School Recruitment Committee (2017/18).
- School Outreach Committee (2016/17).
- School Research Committee (2016/17).
- School Management Committee (2015/16).
- School Learning and Teaching Committee (2015/16).
- School Teaching Quality Group (2015/16).

## Research

**Postdoctoral Fellows:**

- Galatia Cleanthus 2019/20 (main supervisor). School Funded.

**PhD Students:**

- Joseph Dessi 2020/today (main supervisor). School Funded.
- Matina Trachana 2017/today (co-supervisor). School Funded.
- Robbie Bickerton 2015/2019 (main supervisor). EPSRC Funded. School Postgraduate Prize in Pure Maths (2019).
- William Norledge 2014/2017 (co-supervisor). School Funded.

**MPhil Students:**

- Nathan Dixon 2019/today (co-supervisor). School Funded.

**MMath Projects:**

- Frances Bingham 2018/19. Orator for the Graduation Ceremony.
- Chris Barrett 2016/17. Awarded the Best MMath Project School Prize.

**VIVA Examinations:**

- Undrakh Batzorig 2017, Newcastle University (Internal Examiner).
- David Brown 2016, Newcastle University (Internal Examiner).

**Research Interests:**

In the past 50 years, a major trend in Operator Theory focuses on the use of operator algebras for encoding geometrical and topological objects. Operator algebras may be considered as algebras of (bounded in norm) infinite matrices with complex entries. A central aspect of the program is to explore the passage from intrinsic properties of the object into properties of the associated operator algebras, and use invariants of the latter to classify the former. There are two interrelated questions that orientate the course of study:

**(Q.1)**Which (desirable) features of the object determine the operator algebra?**(Q.2)**What is the (desirable) level of equivalence for classifying objects?

Examples of examined objects so far include tilings, tangles, graphs, dynamical systems, groups, semigroups, varieties, homogeneous ideals, and stochastic matrices. My research so far incorporates operator algebras (both selfadjoint and non-selfadjoint) in terms of representation theory, dilation theory, ideal structure, KMS-states theory, C*-envelopes, reflexivity, and hyperrigidity, for objects related to C*-correspondences, product systems, subproduct systems, semigroup actions on operator algebras, dynamical systems, and homogeneous ideals.

## Publications

- Kakariadis ETA. Applications of entropy of product systems: higher-rank graphs.
*Linear Algebra and its Applications*2020,**594**, 124-157. - Kakariadis ETA. Equilibrium states and entropy theory for Nica-Pimsner algebras.
*Advances in Mathematics*2020,**362**, 106940. - Arici F, Kakariadis ETA, Larsen NS. Cuntz-Pimsner Cross-Pollination.
*Nieuw Archief voor Wiskunde*2018,**5/20**, 34-39. - Kakariadis ETA. Finite-dimensional approximations for Nica–Pimsner algebras.
*Ergodic Theory and Dynamical Systems*2019, epub ahead of print. - Kakariadis ETA, Katsoulis EG, Li X. Operator algebras of higher rank numerical semigroups.
*Proceedings of the American Mathematical Society*2020. In Press. - Tandogdu Z, Kakariadis ETA, Naber K, Wagenlehner F, Johansen TEB. Appropriate empiric antibiotic choices in health care associated urinary tract infections in urology departments in Europe from 2006 to 2015: A Bayesian analytical approach applied in a surveillance study.
*PLoS ONE*2019,**14**(4), e0214710. - Dor-On A, Kakariadis ETA. Operator algebras for higher rank analysis and their application to factorial languages. 2018. Submitted.
- Kakariadis ETA. Entropy theory and parametrization for the equilibrium states of Pimsner algebras.
*Journal of Geometry and Physics*2020. In Press. - Davidson KR, Kakariadis ETA. A proof of Boca's Theorem.
*Proceedings of the Royal Society of Edinburgh Section A*2019,**149**(4), 869-876. - Bickerton R, Kakariadis ETA. Free multivariate w*-semicrossed products: reflexivity and the bicommutant property.
*Canadian Journal of Mathematics*2018,**70**(6), 1201-1235. - Barrett C, Kakariadis ETA. On the quantized dynamics of factorial languages.
*Quarterly Journal of Mathematics*2018,**69**(1), 119-152. - Eleftherakis GK, Kakariadis ETA, Katsoulis EG. Morita equivalence of C*-correspondences passes to the related operator algebras.
*Israel Journal of Mathematics*2017,**222**(2), 949-972. - Eleftherakis GK, Kakariadis ETA. Strong Morita equivalence of operator spaces.
*Journal of Mathematical Analysis and Applications*2017,**446**(2), 1632-1653. - Kakariadis ETA, Shalit OM. Operator algebras of monomial ideals in noncommuting variables.
*Journal of Mathematical Analysis and Applications*2018,**472**(1), 738-813. - Kakariadis ETA. On Nica-Pimsner algebras of C*-dynamical systems over \mathbb{Z}_+^n.
*International Mathematics Research Notices*2017,**2017**(4), 1013-1065. - Kakariadis ETA. KMS states on Pimsner algebras associated with C*-dynamical systems.
*Journal of Functional Analysis*2015,**269**(2), 325-354. - Kakariadis ETA, Peters JR. Ergodic extensions of endomorphisms.
*Bulletin of the Australian Mathematical Society*2016,**93**(02), 307-320. - Davidson KR, Fuller AH, Kakariadis ETA. Semicrossed products of operator algebras by semigroups.
*Memoirs of the American Mathematical Society*2017,**247**, 1168. - Davidson KR, Fuller AH, Kakariadis ETA. Semicrossed products of operator algebras: A survey.
*New York Journal of Mathematics*2018,**24a**, 56-86. - Kakariadis ETA. A note on the gauge invariant uniqueness theorem for C*-correspondences.
*Israel Journal of Mathematics*2016,**215**(2), 513-521. - Kakariadis ETA. The Dirichlet property for tensor algebras.
*Bulletin of the London Mathematical Society*2013,**45**(6), 1119-1130. - Kakariadis ETA, Peters JR.
**Representations of C*-dynamical systems implemented by Cuntz families**.*Münster Journal of Mathematics*2013,**6**, 383-411. - Kakariadis ETA, Katsoulis EG. Isomorphism invariants for multivariable C*-dynamics.
*Journal of Noncommutative Geometry*2014,**8**(3), 771-787. - Kakariadis ETA, Katsoulis EG.
**Operator algebras and C*-correspondences: A survey**.*Operator Theory: Advances and Applications*2013,**233**, 45-73. - Kakariadis ETA, Katsoulis EG. C*-algebras and equivalences for C*-correspondences.
*Journal of Functional Analysis*2014,**266**(2), 956-988. - Davidson KR, Kakariadis ETA. Conjugate dynamical systems on C*-algebras.
*International Mathematics Research Notices*2014,**2014**(5), 1289-1311. - Kakariadis ETA. The Šilov Boundary for Operator Spaces.
*Integral Equations and Operator Theory*2013,**76**(1), 25-38. - Kakariadis ETA, Katsoulis EG.
**Contributions to the theory of C*-correspondences with applications to multivariable dynamics**.*Transactions of the American Mathematical Society*2012,**364**(7), 6605-6630. - Kakariadis ETA. Semicrossed products of
*C**-algebras and their C*-envelopes.*Journal d'Analyse Mathématique*2016,**129**(1), 1–31. - Kakariadis ETA, Katsoulis EG.
**Semicrossed products of operator algebras and their C*-envelopes**.*Journal of Functional Analysis*2012,**262**(7), 3108-3124. - Kakariadis ETA.
**Semicrossed products and reflexivity**.*Journal of Operator Theory*2012,**67**(2), 379-395. - Kakariadis ETA.
Greece: University of Athens, 2011.**Operator spaces and operator algebras: Semicrossed products of operator algebras (PhD Thesis)**.