Dr Justin McInroy

Senior Lecturer in Mathematics; Programme Leader for MSc Mathematics

School of Computer and Engineering Sciences
j.mcinroy@chester.ac.uk
Justin McInroy

Justin is a Senior Lecturer in Mathematics and the Programme Leader for the MSc Mathematics programme (postgraduate). He is also an Honorary Research Fellow at the University of Bristol.

Justin is an algebraist with broad interests throughout algebra, group theory and combinatorics, both theoretical and computational.

Justin McInroy joined Chester as a Lecturer in 2022 and was promoted to Senior Lecturer a year later.  He is also currently the Programme Lead for MSc Mathematics. Previously he was at Bristol as a Teaching Associate in Pure Mathematics and for 8 years as a Heilbronn Research Fellow. Before that he was a Teaching Fellow at Leicester and a Lecturer in Pure Mathematics at Lincoln College, Oxford, having completed his PhD at Birmingham.

His Erdos number is 3.

Read more

  • 1st year Computation, Communication and Employability (LaTeX, Python programming and employability skills)
  • 1st year Introduction to Pure Mathematics and Calculus (the calculus part)
  • 2nd year Linear Algebra I
  • 3rd year Group Theory
  • MSc (postgraduate) ICT for Mathematics Research (the Python programming part)

He also supervises a number of 3rd year projects and MSc dissertations.

Justin is a mathematician with broad interests throughout algebra, group theory and combinatorics.

A common theme of his work involves exploring the links between a group of symmetries of an object and the structure of the object itself, such as a geometry or algebra. He uses both theoretical and computation techniques and has extensive experience programming in Python, Magma and GAP.

Recently his research has focused on some interesting classes of non-associative algebra, such as axial algebras. These have motivations coming from mathematical physics, with string theory and VOAs, but examples have recently been found across mathematics including in the theory of non-linear PDEs and Ricci flows on manifolds.

Read more

Please get in contact with Justin if you want to talk mathematics.

arXiv page

MathSciNet page

Quotients of the Highwater algebra and its cover, with Clara Franchi and Mario Mainardis, arXiv:2205.02200, 46 pages, May 2022.

3-generated axial algebras with a minimal Miyamoto group, arXiv:2004.11773, 11 pages, Apr 2020.

Axial algebras of Jordan and Monster type, with Sergey Shpectorov, Proceedings of Groups St Andrews 2022, to appear, arXiv :2209.08043, 40 pages.

From forbidden configurations to a classification of some axial algebras of Monster type, with Sergey Shpectorov, Journal of Algebra 627 (2023), 58–105.

Split spin factor algebras, with Sergey Shpectorov, J. Algebra 595 (2022), 380--397.

Enumerating 3-generated axial algebras of Monster type, with Sanhan Khasraw and Sergey Shpectorov, J. Pure Appl. Algebra 226 (2022), no. 2, 21 pages.

Miyamoto groups of code algebras, with Alonso Castillo-Ramirez, J. Pure Appl. Algebra 225 (2021), no. 6, 19 pages.

An expansion algorithm for constructing axial algebras, with Sergey Shpectorov, J. Algebra 550 (2020), 379--409.

On the structure of axial algebras, with Sanhan Khasraw and Sergey Shpectorov, Trans. Amer. Math. Soc. 373 (2020), 2135--2156.

Code algebras which are axial algebras and their Z_2-gradings, with Alonso Castillo-Ramirez, Isr. J. Math. 233 (2019), 401--438.

Code algebras, axial algebras and VOAs, with Alonso Castillo-Ramirez and Felix Rehren, J. Algebra 518 (2019), 146--176.

Vahlen groups over commutative rings, Math. Z. 284 (2016), no. 3, 901--917.

On Sidki's presentation for orthogonal groups, with Sergey Shpectorov, J. Algebra 434 (2015), 227--248.

An amalgam uniqueness result for recognising q^6:SU_3(q), G_2(q), or 3.M_{10} using biaffine polar spaces, J. Algebra 400 (2014), 105--122.

New flag-transitive geometries for the groups Sp_4(K) and SU_5(K), with Harm Pralle and Sergey Shpectorov, Geom. Dedicata 173 (2014), no. 1, 65--82.

Biaffine polar spaces, Adv. Geom. 13 (2013), no. 3, 449--469.

On the simple connectedness of hyperplane complements in dual polar spaces, II, with Sergey Shpectorov, Discrete Math., 310 (2010), no. 8, 1381--1388.

  • PhD
    University of Birmingham, Birmingham, United Kingdom
  • MMath
    University of Warwick, Coventry, United Kingdom

Read more