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The Centre for Combinatorial Methods in Algebra, Number Theory and Applications (CANTA), headed by Prof Brita Nucinkis, brings together researchers from diverse groups within the departments of Mathematics, Information Security and Computer Science.

Mathematical themes include: 

  • Discrete Mathematics  (Gerke and Moffat)
  • Group Representation Theory (Wildon)
  • Combinatorial and Geometric Group Theory (Barnea, Kar, Nucinkis)
  • Number Theory (Dietmann, McKee, Widmer)
  • Cryptography (Albrecht, Blackburn, Martin, Ng)
  • Quantum Mechanics (Bolte), and
  • Theoretical Computer Science (Gutin, Wahlström).

Strategic aims of CANTA

  • fostering an environment of research excellence for its members by facilitating collaborations within the Centre and with other centres of excellence in the UK and world-wide,
  • supporting grant applications and enhancing training for research students.
  • promoting Knowledge Exchange – members will actively engage with the public particularly with young people to encourage careers in STEM (science, technology, engineering and mathematics).
  • nurturing inter-disciplinary research through exploratory workshops that discuss the influence of its work on the wider research community, e.g. Group Theory in Virology or Stem Cell research.


Our seminars

A series of e-talks and seminars mark the inauguration of the centre. The talks are aimed at a broad audience of mathematicians, mathematical cryptographers, and theoretical computer scientists. To join, please send an email with your full name with CANTA-Launch registration in the subject line to Dr. Martin Widmer You should receive the Zoom link 15 minutes before the talk starts. Please join the meeting with your real name.

The schedule is as follows:

3rd June 2020, 11am (BST): Prof Peter Kropholler, University of Southampton.

Title and Abstract: Amenable groups and Noetherian group rings.

In joint work with Karl Lorensen and Dawid Kielak, we study an old question of Reinhold Baer which dates back to around 1960: which are the groups such that the integral group ring is Noetherian. We shall see that as well satisfying the maximal condition on subgroups (which Baer knew), they also must be amenable. This then connects the question to some interesting Burnside groups constructed by Ivanov and Olshanskii. I love this topic because it touches on two important and apparently very different things in 20th century mathematics: the Banach-Tarski paradox and the roots of non-commutative algebraic geometry.


3rd June 2020, 4pm (BST): Dr Leo Ducas, CWI, Amsterdam. 

Title and abstract: An Algorithmic Reduction Theory for Binary Codes

This is joint work (in Progress) with Thomas Debris-Alazard and Wessel van Woerden. Lattice reduction is the task of finding a basis of short and somewhat orthogonal vectors of a given lattice. In 1985 Lenstra, Lenstra and Lovasz proposed a polynomial time algorithm for this task, with an application to factoring rational polynomials. Since then, the LLL algorithm has found countless application in algorithmic number theory and in cryptanalysis.

There are many analogies to be drawn between Euclidean lattices and linear codes over finite fields. In this work, we propose to extend the range of these analogies by considering the task of reducing the basis of a binary code. In fact, all it takes is to choose the adequate notion mimicking Euclidean orthogonality (namely orthopodality), after which, all the required notions, arguments, and algorithms unfold before us, in quasi-perfect analogy with lattices.


10th June 2020, 4pm (BST): Prof Lillian Pierce, Duke University.

To show our support for the Black Lives Matter movement we have decided to postpone the CANTA-Launch talk of Lillian Pierce to June 11th 4pm (BST).

Title and Abstract: On some open questions in number theory: from the perspective of moments

Many questions in number theory can be phrased loosely in the following terms: “how often can this function take large values?” We will talk about some open questions in number theory where we want to show that the answer is “never.” In particular, we will discuss some interesting situations where we can upgrade information that a function “rarely takes large values” to information that it “never takes large values.” This perspective allows us to see some new connections between open conjectures in number theory.


The virtual seminar meets every Wednesday at 2PM unless advertised otherwise. The Schedule includes instructions on how to join. 

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