Mathematics and Statistics

Photo of Dr Ilaria Colazzo

Dr Ilaria Colazzo

Postdoctoral Research Fellow

 I.Colazzo@exeter.ac.uk

 (Streatham) 5280

 01392 725280

Overview

Currently, I am a postdoctoral research fellow at the University of Exeter (UK). I am working on the EPSRC project: Hopf-Galois Theory and Skew Braces (PI: Prof. N. Byott).

Previously, I was a postdoctoral researcher at the Vrije Universiteit Brussel (VUB) in the group of ALGB: Algebra, Incidence Geometry (Group and Semigroup Theory) headed by Prof. E. Jespers.

I completed my PhD in 2017 at the University of Salento under the supervision of Prof. F. Catino. During my PhD, I was a visiting PhD student at the University of Warsaw in the group of Algebra and Number Theory headed by Prof. J. Okniński.

My PhD thesis focuses on studying a novel algebraic structure, namely semi-brace, and its connection with set-theoretical solutions of the Yang-Baxter equation.

My research interest focuses on studying algebraic structures associated with discrete versions of some equations in mathematical physics, such as the Yang-Baxter equation and the Pentagon equation. I am mainly interested in algebraic structures such as skew braces, trusses and generalisations that organise, classify and help to find solutions of the Yang-Baxter equation and the Pentagon equation with given properties.

Back to top

Publications

Copyright Notice: Any articles made available for download are for personal use only. Any other use requires prior permission of the author and the copyright holder.

| 2023 | 2022 | 2021 | 2020 | 2019 | 2017 | 2016 | 2015 |

2023

  • Colazzo I, Jespers E, Kubat Ł, Antwerpen AV. (2023) Simple solutions of the Yang-Baxter equation. [PDF]
  • Brzeziński T, Colazzo I, Doikou A, Vendramin L. (2023) Mini-Workshop: Skew Braces and the Yang–Baxter Equation, Oberwolfach Reports, volume 20, no. 1, pages 537-563, DOI:10.4171/owr/2023/9.
  • Colazzo I, Jespers E, Kubat Ł, Van Antwerpen A, Verwimp C. (2023) Finite Idempotent Set-Theoretic Solutions of the Yang–Baxter Equation, International Mathematics Research Notices, volume 2024, no. 7, pages 5458-5489, DOI:10.1093/imrn/rnad183. [PDF]
  • Colazzo I, Jespers E, Kubat Ł, Antwerpen AV. (2023) Structure algebras of finite set-theoretic solutions of the Yang--Baxter equation. [PDF]

2022

  • Colazzo I, Jespers E, Kubat Ł, Antwerpen AV, Verwimp C. (2022) Finite idempotent set-theoretic solutions of the Yang--Baxter equation. [PDF]
  • Colazzo I, Ferrara M, Trombetti M. (2022) On derived-indecomposable solutions of the Yang--Baxter equation.
  • Colazzo I, Jespers E, Van Antwerpen A, Verwimp C. (2022) Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and semitrusses, Journal of Algebra, volume 610, pages 409-462, DOI:10.1016/j.jalgebra.2022.07.019. [PDF]

2021

  • Colazzo I, Jespers E, Antwerpen AV, Verwimp C. (2021) Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and semitrusses, Journal of Algebra, volume 6, no. 0, pages 409-462. [PDF]
  • Colazzo I. (2021) Skew braces and solutions of the Yang-Baxter equation, Hopf algebras and Galois module theory, 24th - 27th May 2021.
  • Catino F, Colazzo I, Stefanelli P. (2021) Set-theoretic solutions to the Yang–Baxter equation and generalized semi-braces, Forum Mathematicum, volume 33, no. 3, pages 757-772, DOI:10.1515/forum-2020-0082. [PDF]
  • Colazzo I, Van Antwerpen A. (2021) The algebraic structure of left semi-trusses, Journal of Pure and Applied Algebra, volume 225, no. 2, DOI:10.1016/j.jpaa.2020.106467.

2020

2019

  • Catino F, Colazzo I, Stefanelli P. (2019) The matched product of the solutions to the Yang-Baxter equation of finite order, DOI:10.48550/arxiv.1904.07557.
  • Colazzo I, Van Antwerpen A. (2019) The algebraic structure of left semi-trusses, DOI:10.48550/arxiv.1908.11744.
  • Catino F, Colazzo I, Stefanelli P. (2019) The matched product of set-theoretical solutions associated with shelves. [PDF]
  • Colazzo I. (2019) Braces: between regular subgroups and solutions of the Yang-Baxter equation, 1st workshop Algebra for Cryptography, L'aquila (italy), 10th - 11th Oct 2019.
  • Colazzo I. (2019) The matched product of shelves, Advances in Group Theory and Applications 2019, Lecce (italy), 25th - 28th Jun 2019.
  • Catino F, Colazzo I, Stefanelli P. (2019) Skew left braces with non-trivial annihilator, Journal of Algebra and its Applications, volume 18, no. 2, DOI:10.1142/S0219498819500336.

2017

2016

2015

Back to top

Further information

Conferences and seminars

Organised seminars and conferences

26/02–03/03/2023, Oberwolfach mini-workshop (2309a): Skew Braces and the Yang–Baxter Equation, member of the scientific committee (with T. Brzezinski, A. Doikou, and L. Vendramin)

10-16/07/2019, The algebra of the Yang–Baxter equation, Bedlewo (Poland), member of the organising committee (with Ł. Kubat, V. Lebed, J. Okniński, A. Van Antwerpen, L. Vendramin, and M. Wiertel)

16-19/09/2019, Conference Young Researchers Algebra Conference 2019, Naples (Italy), member of the scientific committee (with M. Brescia, M. Ferrara, P. Stefanelli and M. Trombetti)

25-28/06/2019, Advances in Group Theory and Applications 2019, Lecce (Italy), member of the organising committee (with M. Brescia, M. Ferrara, M. M. Miccoli, P. Stefanelli and M. Trombetti)

05-08/09/2017, Advances in Group Theory and Applications 2017, Lecce (Italy), member of the organising committee (with M. M. Miccoli, P. Stefanelli and M. Trombetti)

16–19/06/2015, Advances in Group Theory and Applications 2015, Porto Cesareo, Lecce (Italy), member of the organising committee (with M. M. Miccoli, P. Stefanelli)

2015–2019, Algebra Reading Seminar, Co-organiser of the Department seminar (with F. Catino)
University of Salento, Department of Mathematics and Physics “Ennio De Giorgi”

Talks

20/10/2022, Seminar Algebra, University of Warsaw (Poland)
Retractability problem for quasi-linear cycle sets – Invited talk

30/05–03/06/2022, Hopf algebras and Galois module theory, Omaha/Online
YB-semitrusses and left non-degenerate solutions to the Yang-Baxter equation – Invited talk

18/05/2022, QA Seminar, Vrije Universiteit Brussel (Belgium)
Set-theoretic solution of the Pentagon Equation: the involutive case – Invited talk

20/04/2022, University of Padua (Italy)
Set-theoretic solutions of the Yang-Baxter equation and related associative structure – Invited talk

04–06/01/2022, Braces in Bracelet Bay, Swansea University, Online
YB-semitrusses with associated bijective solutions – Invited talk

12/11/2021, Al@Bicocca take-away, University of Milan - Bicocca, Milan (Italy)
Bijective set-theoretic solutions of the Pentagon Equation – Invited talk

24–27/05/2021, Hopf algebras and Galois module theory, Online
Skew braces and solutions of the Yang-Baxter equation – Invited talk

28/05/2020, ALGB Seminar, Vrije Universiteit Brussel (Belgium)
Involutive solutions of the Pentagon Equation – Invited talk

11/02/2020, ALGB Seminar, Vrije Universiteit Brussel (Belgium)
The algebraic structure of brace-like semi-trusses – Invited talk

10–11/10/2019, 1st workshop Algebra for Cryptography, L'Aquila (Italy)
Braces: between regular subgroups and solutions of the Yang-Baxter equation – Invited talk

25–28/06/2019, Advances in Group Theory and Applications 2019, Lecce (Italy)
The matched product of shelves

13/10/2018, ALGB Seminar, Vrije Universiteit Brussel (Belgium)
Regular subgroups and left semi-braces – Invited talk

11–15/03/2018, Noncommutative and non-associative structures, braces and applications, Malta
The matched product of the solutions of the Yang-Baxter equation – Invited talk

5–8/09/2017, Advances in Group Theory and Applications 2017, Lecce (Italy)
Skew braces with non-trivial annihilator

18–24/06/2017, Groups, Rings and the Yang-Baxter equation, Spa (Belgium)
Semi-braces and the Yang-Baxter equation

23–24/05/2017, Young Researchers Algebra Conference 2017, Naples (Italy)
The algebraic structure of semi-brace

24/11/2016, Seminar Algebra, University of Warsaw (Poland)
Regular subgroups of the affine group – Invited talk

3–8/07/2016, Conference on Rings and Polynomials, Graz (Austria)
Radical braces and the Yang–Baxter equation

16-17/06/2016, Group Theory in Florence: a meeting in honour of Guido Zappa, Florence (Italy)
Regular subgroups of an affine group

16–19/06/2015, Advances in Group Theory and Applications 2015, Porto Cesareo, Lecce (Italy)
The Asymmetric Product of radical braces

Teaching

  • A.Y. 2022–23
  • A.Y. 2021–22
    • MTH1001 – Mathematical structures (Course Dr Gihan Marasingha)
      Tutor (for a total of 10 hours)
      Duties included preparing lectures for tutorial classes, fielding of student inquiries, and marking homework.
      Univeristy of Exeter, Exeter (UK)
  • A.Y. 2018–19
    • Algebra I and II (Course Prof. F. Catino and Prof. M. M. Miccoli)
      Tutor (for a total of 30 hours)
      Duties included preparing lectures for tutorial classes, fielding of student inquiries, and office hours.
      Università del Salento, Lecce (Italy)
  • A.Y. 2017–18
    • Group Theory (Course Prof. F. Catino)
      Teaching assistant
      Duties included preparing lectures for tutorial classes for recitation classes and office hours.
      Università del Salento, Lecce (Italy)
    • Mathematics preliminary course for bachelor’s students in Mathematics and in Physics
      Instructor (for a total of 30 hours)
      Duties included preparing lectures, fielding of student inquiries, and office hours.
      Università del Salento, Lecce (Italy)
  • A.Y. 2016–17
    • Group Theory (Course Professor F. Catino)
      Teaching assistant
      Duties included preparing lectures for tutorial classes for recitation classes and office hours.
      Università del Salento, Lecce (Italy)
    • Algebra I (Course Professor F. Catino)
      Tutor (for a total of 30 hours)
      Duties included preparing lectures for tutorial classes, fielding of student inquiries, and office hours.
      Università del Salento, Lecce (Italy)
  • A.Y. 2015–16
    • Group Theory (Course Prof. F. Catino)
      Teaching assistant
      Duties included preparing lectures for tutorial classes for recitation classes and office hours.
      Università del Salento, Lecce (Italy)
    • Algebra II (Prof. M. M. Miccoli)
      Teaching assistant
      Duties included preparing lectures for tutorial classes for recitation classes and office hours.
      Università del Salento, Lecce (Italy)
  • July 2016 – 2019
    Exam committee member for Algebra examination (it "Cultore della materia")
    Duties included grading final exams.
    Università del Salento, Lecce (Italy)

Back to top