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Research lectures, seminars and events

The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but  wish to enquire about attending one of the events please contact the organiser or host department.

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Events for 19 November 2020

Managing Leishmania donovani infection through immunobiological approaches for innovative diagnosis, prevention and cure

1:00pm, Via Zoom, Dr Nahid Ali, IICB, India

Mauricio Bustamante: Diffeomorphisms of solid tori

1:00pm, Zoom.

The homotopy groups of the diffeomorphism group of a high dimensional manifold with infinite fundamental group can be infinitely generated. The simplest example of this sort is the solid torus $T=S^1\times D^{d-1}$. In fact, using Hatcher, Igusa, and Waldhausen's approach to pseudoisotopy theory, it is possible to show that in the range of degrees up to (roughly) $d/3$, the homotopy groups of $Diff(T)$ contain infinitely generated torsion subgroups.

In this talk, I will discuss an alternative point of view to study $Diff(T)$ which does not invoke pseudoisotopy theory: when $d=2n$, we interpret $Diff(T)$ as the "difference" between diffeomorphisms and certain self-embeddings of the manifold $X_g$ which is the connected sum of $T$ with the g-fold connected sum of $S^n \times S^n$.

We will see how infinitely generated torsion subgroups appear from this perspective, and that they can be found even up to degrees $d/2$. This is ongoing joint work with O. Randal-Williams.

2:30pm, Zoom