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16:00 - 17:00 25 November 2015
What makes something special?
UCL Student Union Building
25 Gordon Street | London | WC1H 0AY | United Kingdom
In geometry - algebraic geometry in particular, certain objects can naturally be called ‘special’. This usually means that they possess extra symmetries that make them stand out from the rest. For example such objects may be acted upon transitively by a certain group. It is desirable (from both theoretical and practical points of view) to be able to characterise these special objects by a property verifiable in practice. They may be characterised by the property of containing many points of a special type. There are other characterisations - they may be characterised by their ‘bi-algebraic nature’ or in terms of Riemannian geometry (they are totally geodesic manifolds). Proving equivalences between such characterisations is often a difficult (and in some cases unsolved) problem. My research has been mainly concerned with this type of problem. I will present concrete examples, review conjectures and results related to characterisations of ‘special objects’.
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