Transpennine Topology Triangle

Thursday 14th July 2016

J11 is on J floor of the Hicks building. LT3 is on floor D (ground floor) of the Hicks Building.

Tea and coffee breaks will be in the common room (I15) on I floor of the Hicks Building.

10:30 - 11:00 | Tea/coffee |

11:00 - 12:00 J11 | Neil Strickland (Sheffield) An example in the geometry of surfaces |

12:00 - 14:00 | Lunch |

14:00 - 15:00 LT3 | Yumi Boote (Manchester) Symmetric squares of even spaces |

15:00 - 16:00 | Tea/coffee |

16:00 - 17:00 J11 | Chris Braun (Lancaster) Derived localisation |

Abstracts of talks

Speaker: Yumi Boote (Manchester)

Title: Symmetric squares of even spaces

Abstract: The integral homology of the symmetric square of a CW complex has been known since 1960’s, although the general answer is very complicated. However, the situation for the integral cohomology ring remains an open problem, except for a few special cases. One of the main difficulties is the computation of its multiplicative structure. In this talk I shall outline the solution for even spaces; these have torsion free integral cohomology, concentrated in even dimensions. Examples include quaternionic projective spaces, the octonionic projective plane, and flag manifolds.

Speaker: Chris Braun (Lancaster)

Title: Derived localisation

Abstract: Localisation of commutative rings and modules is among the fundamental tools of commutative algebra and algebraic geometry. It has been well-understood and documented for a long time. On the other hand, localisation of noncommutative rings, or even categories, although more fundamental, is less well-understood and less well-behaved. It appears in many contexts, indeed the homotopy category of spaces is the localisation with respect to weak equivalences and so in this sense noncommutative localisation is central in homotopy theory. Embracing a, by now well established, philosophy from homotopy theory and working with a derived version of noncommutative localisation allows us to obtain a better behaved theory of noncommutative localisation, employing methods from homotopical algebra. In this theory, the localisation of a dg algebra, or more generally a dg category, can be seen to be, in a certain precise sense, equivalent to the Bousfield localisation of its category of dg modules. This general abstract result has a wide range of concrete applications to, among others, a general version of the group completion theorem, the K–theory localisation sequence as well as having consequences for the localisation of usual commutative rings.

Speaker: Neil Strickland (Sheffield)

Title: An example in the geometry of surfaces

Abstract:

Everyone who wishes to participate is welcome, particularly postgraduate students. The usual criteria for assistance with travel expenses apply. Beneficiaries will need to complete the standard forms, which are available at the TTT Homepage.