Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
7 May 2018
Benjamin J. Barrett

When studying a group, it is natural and often useful to try to cut it up 
onto simpler pieces. Sometimes this can be done in an entirely canonical 
way analogous to the JSJ decomposition of a 3-manifold, in which the 
collection of tori along which the manifold is cut is unique up to isotopy. 
It is a theorem of Brian Bowditch that if the group acts nicely on a metric 
space with a negative curvature property then a canonical decomposition can 
be read directly from the large-scale geometry of that space. In this talk 
we shall explore an algorithmic consequence of this relationship between 
the large-scale geometry of the group and is algebraic decomposition.

7 May 2018
Dominic Joyce

 Suppose A is a nice abelian category (such as coherent sheaves coh(X) on a smooth complex projective variety X, or representations mod-CQ of a quiver Q) or T is a nice triangulated category (such as D^bcoh(X) or D^bmod-CQ) over C. Let M be the moduli stack of objects in A or T. Consider the homology H_*(M) over some ring R.
  Given a little extra data on M, for which there are natural choices in our examples, I will explain how to define the structure of a graded vertex algebra on H_*(M). By a standard construction, one can then define a graded Lie algebra from the vertex algebra; roughly speaking, this is a Lie algebra structure on the homology H_*(M^{pl}) of a "projective linear” version M^{pl} of the moduli stack M.
  For example, if we take T = D^bmod-CQ, the vertex algebra H_*(M) is the lattice vertex algebra attached to the dimension vector lattice Z^{Q_0} of Q with the symmetrized intersection form. The degree zero part of the graded Lie algebra contains the associated Kac-Moody algebra.
  The construction appears to be new, but is connected with a lot of work in Geometric Representation Theory, to do with Ringel-Hall-type algebras and their representations, such as the results of Grojnowski-Nakajima on Hilbert schemes. The vertex algebra construction is enormously general, and applies in huge classes of examples. There is a differential-geometric version too.
  The question I am hoping someone in the audience will answer is this: what is the physical interpretation of these vertex algebras?
  It is in some sense an "even Calabi-Yau” construction: when applied to coh(X) or D^bcoh(X), it is most natural for X a Calabi-Yau 2-fold or Calabi-Yau 4-fold, and is essentially trivial for X a Calabi-Yau 3-fold. I discovered it when I was investigating wall-crossing for Donaldson-Thomas type invariants for Calabi-Yau 4-folds. So perhaps one should look for an explanation in the physics of Calabi-Yau 2-folds or 4-folds, with M the moduli space of boundary conditions for the associated SCFT.

  • String Theory Seminar
8 May 2018
Afaf Bouharguane

We consider numerical methods for solving  time dependent partial differential equations with convection-diffusion terms and anti-diffusive fractional operator of order $\alpha \in (1,2)$. These equations are motivated by two distinct applications: a dune morphodynamics model and a signal filtering method. 
We propose numerical schemes based on local discontinuous Galerkin methods to approximate the solutions of these equations. Numerical stability and convergence of these schemes are investigated. 
Finally numerical experiments are given to illustrate qualitative behaviors of solutions for both applications and to confirme the convergence results. 

  • Numerical Analysis Group Internal Seminar
8 May 2018
Brigitte Stenhouse

Part of the series 'What do historians of mathematics do?'

In 1873 the Personal Recollections from Early Life to Old Age of Mary Somerville were published, containing detailed descriptions of her life as a 19th century philosopher, mathematician and advocate of women's rights. In an early draft of this work, Somerville reiterated the widely held view that a fundamental difference between men and women was the latter's lack of originality, or 'genius'.

In my talk I will examine how Somerville's view was influenced by the historic treatment of women, both within scientific research, scientific institutions and wider society. By building on my doctoral research I will also suggest an alternative viewpoint in which her work in the differential calculus can be seen as original, with a focus on her 1834 treatise On the Theory of Differences.

  • History of Mathematics


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