From 14 to 19 of January 2019, Dr Colin Reid from the University of Newcastle in Australia was visiting Simon Smith to continue work on their project to understand the local-to-global behaviour of groups acting on trees that enjoy the Independence Property P described by J. Tits.…]]>

Charlotte Scott Centre for Algebra

From 14 to 19 of January 2019, Dr Colin Reid from the University of Newcastle in Australia was visiting Simon Smith to continue work on their project to understand the local-to-global behaviour of groups acting on trees that enjoy the Independence Property P described by J. Tits.

Colin’s visit was funded by the London Mathematical Society, as part of a “Research in Pairs” grant that Colin and Simon were awarded in June 2018.

On Wednesday 16 January Dr Reid gave a talk to the Charlotte Scott Centre for Algebra in Lincoln on “*Locally compact piecewise full groups*“.

An update for the current 19th edition of “Kourovka Notebook (Unsolved Problems in Group Theory)” is posted. Several problems, both from the latest section and from the previous ones, have now been solved. (But of course many problems remain very much open:-).) Recall that “Kourovka Notebook” is a famous collection of open…]]>

Charlotte Scott Centre for Algebra

An update for the current 19th edition of “Kourovka Notebook (Unsolved Problems in Group Theory)” is posted. Several problems, both from the latest section and from the previous ones, have now been solved. (But of course many problems remain very much open:-).)

Lincoln’s School of Mathematics and Physics wishes a happy new year 2019 to all staff, students, friends and followers!

]]>On Wednesday the 5th of December 2018 Dr Tim Dokchitser (University of Bristol) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk “Brauer relations”. Abstract: “If G is a finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. These…]]>

Charlotte Scott Centre for Algebra

On Wednesday the 5th of December 2018 **Dr Tim Dokchitser** (University of Bristol) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk “*Brauer relations*”.

Abstract: “If G is a finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. These phenomena are called `Brauer relations’ or `linearly equivalent G-sets’, and they turn out to have interesting applications in number theory. I will explain how to classify Brauer relations in all finite groups, the history of the problem and some number-theoretic applications. This is joint work with Alex Bartel.”

On Wednesday the 5th of December 2018 Dr Vladimir Dokchitser (King’s College, University of London) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk “Ranks of Elliptic Curves”. Abstract: “I will discuss elliptic curves from the classical number theoretic point of view of trying…]]>

Charlotte Scott Centre for Algebra

On Wednesday the 5th of December 2018 **Dr Vladimir Dokchitser** (King’s College, University of London) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk “*Ranks of Elliptic Curves*”.

Abstract: “I will discuss elliptic curves from the classical number theoretic point of view of trying to solve Diophantine equations. The aim will be both to explain how we think about these creatures and to give an overview of what we can (and sometimes can’t) prove about them, and to illustrate it with explicit examples. I will not try to describe the huge modern technical machine that has been developed to study elliptic curves, so most of the results will come as black boxes.”

On Wednesday the 30th of January 2019, David Stewart (Newcastle University) will be visiting the Charlotte Scott Centre for Algebra and giving a seminar on Gröbner bases, smooth centralisers and the Lefschetz principle. His talk will be at 3pm in INB 3305. All are welcome. His talk abstract…]]>

Charlotte Scott Centre for Algebra

On Wednesday the 30th of January 2019, David Stewart (Newcastle University) will be visiting the Charlotte Scott Centre for Algebra and giving a seminar on Gröbner bases, smooth centralisers and the Lefschetz principle. His talk will be at 3pm in INB 3305. All are welcome.

His talk abstract is as follows:

“(Joint with Ben Martin and Lewis Topley). In a paper in the now defunct LMS Journal of Computation I used GAP to compute the Lie-theoretic centralisers in the exceptional groups of elements in their minimal modules in all characteristics, establishing when the centralisers in the groups were smooth. Non-smoothness was only found in very small characteristics, even where there are infinitely many orbits. This led to a question on when all centralisers of elements in a Z-defined representation would be smooth if the characteristic were large enough. With my co-authors we managed to prove this using the Lefschetz principle from…

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Anitha Thillaisundaram recently obtained a Staff Mobility Award from the Lincoln Institute of Advanced Studies. This research grant is to initiate a new collaboration on branch groups with Gustavo Fernandez-Alcober at the University of the Basque Country, Bilbao.]]>

Charlotte Scott Centre for Algebra

Anitha Thillaisundaram recently obtained a Staff Mobility Award from the Lincoln Institute of Advanced Studies. This research grant is to initiate a new collaboration on branch groups with Gustavo Fernandez-Alcober at the University of the Basque Country, Bilbao.

A short article discussing the implications of the Gaia spacecraft on future interstellar travel by Dr Phil Sutton is published in Principium, the quarterly newsletter of the Initiative for Interstellar Studies. Here, we consider how understanding the positions and movement of stars within our galaxy is important for future missions that…]]>

A short article discussing the implications of the Gaia spacecraft on future interstellar travel by Dr Phil Sutton is published in Principium, the quarterly newsletter of the Initiative for Interstellar Studies.

Here, we consider how understanding the positions and movement of stars within our galaxy is important for future missions that might travel beyond our own solar system. One key thing to consider is that stars do not move on Keplerian orbits about the galactic centre and are difficult to understand. Part of this non-Keplerian motion comes a random relative velocity that increases in time due to close encounters with other stars. However, some of the movement of the stars in the galaxy is influenced by dark matter and its distribution. Better understanding how the stars move in our galaxy can help us map out the dark matter more accurately and in turn guide our spacecraft to other stars, at…

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On 5th of December 2018 we had our first ever Physics Alumni Event in The Cardinal’s Hat. The event consisted of a short lecture by Dr Phil Sutton entitled “Exotic New Worlds”, which looked at some recently discovered exoplanets, and was followed by an extensive discussion and networking with our…]]>

On 5th of December 2018 we had our first ever Physics Alumni Event in The Cardinal’s Hat. The event consisted of a short lecture by Dr Phil Sutton entitled “Exotic New Worlds”, which looked at some recently discovered exoplanets, and was followed by an extensive discussion and networking with our physics graduates as well current MPhys students.

On Wednesday the 28th of November 2018, Dr Nick Gill (University of South Wales) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk “Cherlin’s conjecture for finite binary permutation groups”. Abstract: “A mathematical object C is called HOMOGENEOUS if any local symmetry can be extended…]]>

Charlotte Scott Centre for Algebra

On Wednesday the 28th of November 2018, **Dr Nick Gill** (University of South Wales) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk “*Cherlin’s conjecture for finite binary permutation groups*”.

Abstract: “A mathematical object C is called HOMOGENEOUS if any local symmetry can be extended to a symmetry of C itself. The category of vector spaces, for instance, is replete with homogeneous objects: if U_1 and U_2 are vector subspaces of V that are symmetric, i.e. there is an invertible linear transformation T between them, then we know that we can extend T to an invertible linear transformation V -> V.

In other categories, though, homogeneous objects are hard to find — for instance, if one considers the category of graphs, a classical theorem of Sheehan/ Gardiner tells us that there are only a couple of infinite families, plus a couple of sporadic examples. Our…

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