Past Topology Seminar

I will present a general formalism for understanding coloured operads of different flavours, such as cyclic operads, modular operads and topological field theories. The talk is based on arXiv:math/0701767.

Roughly speaking, a quasiregular map is a possibly-branched covering map with bounded distortion. The theory of such maps was developed in the 1970s to carry over to higher dimensions the more geometric aspects of the theory of complex analytic functions of the plane. In this talk I shall outline the proof of rigidity theorems describing the quasiregular self-maps of hyperbolic manifolds. These results rely on an extension of Sela's work concerning the stability of self-maps of hyperbolic groups, and on older topological ideas concerning discrete-open and light-open maps, particularly their effect on fundamental groups. I shall explain how these two sets of ideas also lead to topological rigidity theorems. This talk is based on a paper with a similar title by Bridson, Hinkkanen and Martin (to appear in Compositio shortly). http://www2.maths.ox.ac.uk/~bridson/papers/QRhyp/

  In this talk I will show how one can sometimes "uncomplete" the p-completed classifying space of a finite group, to obtain the original (non-completed) classifying space, and hence the original finite group. This "uncompletion" process is closely related to well-known local-to-global questions in group theory, such as the classification of finite simple groups. The approach goes via the theory of p-local finite groups. This talk is a report on joint work with Bob Oliver.  

There is a construction, due to Kontsevich, which produces cohomology classes in moduli spaces of Riemann surfaces from the initial data of an A-infinity algebra with an invariant inner product -- a kind of homotopy theoretic notion of a Frobenius algebra.

In this talk I will describe a version of this construction based on noncommutative symplectic geometry and use it to show that homotopy equivalent A-infinity algebras give rise to cohomologous classes. I will explain how the whole framework can be adapted to deal with Topological Conformal Field Theories in the sense of Costello, Kontsevich and Segal.

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