Forthcoming events in this series
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Lattices in Simple Lie Groups: A Survey
Abstract
Lattices in semisimple Lie groups have been studied from the point of view of number theory, algebraic groups, topology and geometry, and geometric group theory. The Fragestellung of one line of investigation is to what extent the properties of the lattice determine, and are determined by, the properties of the group. This talk reviews a number of results about lattices, and in particular looks at Mostow--Margulis rigidity.
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$\pi$-convergence: The dynamics of isometries of Hadamard spaces on the boundary
Abstract
It a classical result from Kleinian groups that a discrete group, $G$, of isometries of hyperbolic k-space $\Bbb H^k$ will act on the
boundary sphere, $S^{k-1}$, of $\Bbb H^k$ as a convergence group.
That is:
For every sequence of distinct isometries $(g_i)\subset G$ there is a subsequence ${g_i{_j})$ and points $n,p \in \S^{k-1}$ such that for $ x \in S^{k-1} -\{n\}$, $g_i_{j}(x) \to p$ uniformly on compact subsets
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Monoids of moduli spaces of manifolds
Abstract
Joint work with Soren Galatius. We study categories C of d-dimensional cobordisms, from the perspective of Galatius, Madsen, Tillmann and Weiss. Their main result is the determination of the homotopy type of the classifying-space of such cobordism categories, as the infinite loop space of a certain Thom spectrum. One can investigate subcategories D of C having the property that the classifying-space BD is equivalent to BC, the smaller such D one can find the better.
We prove that in may cases of interest, D can be taken to be a homotopy commutative monoid. As a consequence, the stable cohomology of many moduli spaces of surfaces can be identified with that of the infinite loop space of certain Thom spectra.
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Riemann surfaces with conical points: monodromy and the Weil- Petersson Poisson structure
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Apologies, Lecture cancelled
Abstract
Open Riemann surfaces and the Weil-Petersson Poisson structure
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