The quotient of a group G by the normal closure N of all its torsion elements T need not be torsion-free. However, iterating this process a countably-infinite number of times yields the universal torsion-free quotient of G. With this in mind, we define the Torsion Length of a group to be the minimum number of such quotients needed to yield a torsion-free group (or \omega if no such number exists). Finding examples of groups with infinite torsion length is somewhat tricky, especially if one restricts to finitely presented, or even finitely generated groups. I’ll aim to discuss some of these examples, and give an overview of how the constructions work.

This is a joint work with Rishi Vyas. ]]>

*Abstract*: Cayley graphs of finite groups are a rich source of examples of sparse graphs of small diameter, which are of interest in cryptography, computational group theory and various combinatorial puzzles. In such applications one often further asks for a fast “navigation” algorithm, that is an algorithm which writes a given element of the group as a short word in a generating set. In this talk I will introduce a framework for the design and analysis of such algorithms in many familiar finite groups, using tools from pro-*p* group theory.

On 12 December Dr Jonathan Crofts from Nottingham Trent University gave a seminar on “Complex brain networks in health, development and disease”, as part…]]>

On 12 December Dr Jonathan Crofts from Nottingham Trent University gave a seminar on “Complex brain networks in health, development and disease”, as part of the 3rd year undergraduate “Advanced Topics Of Mathematics and Mathematics Seminar” module at the University of Lincoln. This final talk in the seminar series in Semester 1 drew considerable interest from the students and members of staff. The speaker demonstrated how mathematical methods of linear algebra, network science can be used in various applications to neuroscience and brain diseases, as well as to other social and technological networks.

On Wednesday the 20th of December 2017, Henry Bradford, from the Georg-August-Universität Göttingen, will be visiting Lincoln and giving a seminar at 2.30pm in INB 3305.

His talk title is “Diameter & Navigation in Finite Cayley Graphs” and his talk abstract is as follows: “Cayley graphs of finite groups are a rich source of examples of sparse graphs of small diameter, which are of interest in cryptography, computational group theory and various combinatorial puzzles. In such applications one often further asks for a fast “navigation” algorithm, that is an algorithm which writes a given element of the group as a short word in a generating set. In this talk I will introduce a framework for the design and analysis of such algorithms in many familiar finite groups, using tools from pro-p group theory.”

]]>Simon Smith visited Adrien Le Boudec and Pierre-Emmanuel Caprace at the Université Catholique de Louvain (UCL) in Belgium from 26th November until 30th November 2017. While there he gave a lecture on his research, and had a number of stimulating and very useful conversations with members of the research group. He also found a public statue that might appeal to University of Lincoln’s Sandro Mattarei…

]]>On 14 December 2017 we held our largest School Christmas Party with food, drinks, music and even Xmas quiz. For the first time…]]>

On 14 December 2017 we held our largest School Christmas Party with food, drinks, music and even Xmas quiz. For the first time we had students from the whole 3 years of study! The winner of the Xmas Quiz was a team of our 3rd year Physics students!

Modern, non-invasive brain imaging techniques are providing unparalleled access into the living human brain, and the emergent complex data sets describing global architectures, of both structure and function, open up fascinating opportunities to characterise and understand what is perhaps nature’s most complex system. Recently, a number of studies have shown that brain injury and disease manifest via faulty, disrupted brain networks (e.g. schizophrenia, Alzheimer’s disease, multiple sclerosis and stroke). Yet, despite significant progress in our understanding of human brain connectivity over the past decade, clinical applications of network analysis of the brain are still in their infancy. In this talk, I shall provide an overview of the state-of-the-art in complex network applications to clinical neuroscience, before considering a number of recent extensions in the area, the aim of which is to construct more physiologically realistic network models of the human brain via a combined theoretical/experimental approach.

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Is algebra a spoilsport in mathematics? a public lecture by Professor Evgeny Khukhro University of Lincoln Wednesday, 17 January 2018, 6:00-7:20 pm Newton…]]>

Distinguished Maths & Physics Public Lectures

Is it the role of algebra to be taking fun out of mathematics? Starting from primary school level, there are numerous examples in which lively mathematical problems are “dried up” by algebra. Or could one experience a different, sublime kind of satisfaction from application of algebraic methods? I will discuss these questions both from the historical perspective and on the basis of personal experience.

Evgeny Khukhro is a Professor of Pure Mathematics in School of Mathematics and Physics of University of Lincoln. Evgeny received his PhD in 1980 in algebra from Novosibirsk University, Russia, and DSc (Habilitation) in 1988 in group theory from Sobolev Institute of Mathematics of Siberian Branch of Russian Academy of Sciences…

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