Transpennine Topology Triangle

Friday 11th March 2016

The talks will take place in the Michael Atiyah Building (MAB119), with tea/coffee in the same place.

University of Leicester Campus Map: http://www2.le.ac.uk/

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

11:30 - 12:30 | Scott Balchin (Leicester) Crossed Simplicial Group Constructions |

12:30 - 14:00 | Lunch |

14:00 - 15:00 | Carmelo Di Natale (Newcastle) Hodge Theory and Deformations of Affine Cones of Subcanonical Projective Varieties |

15:00 - 15:30 | Tea/coffee |

15:30 - 17:00 | Andreas Holmstrom (Ålesund) An elementary approach to motives |

Abstracts of talks

Speaker: Scott Balchin (Leicester)

Title: Crossed Simplicial Group Constructions

Abstract: Crossed simplicial groups were introduced by Loday and Fiedorowicz (and independently by Krasauskas under the name of skew-simplicial sets). These are categories which extend the simplicial category and allow us to have natural group actions on each level of the simplicial structure. One of the most recognised crossed simplicial groups is Connes cyclic category. In this talk we will look at extending the nerve and bar constructions of groups to a general crossed simplicial group, and if time allows, discuss some possible avenues of research involving crossed simplicial groups.

Speaker: Carmelo Di Natale (Newcastle)

Title: Hodge Theory and Deformations of Affine Cones of Subcanonical Projective Varieties

Abstract: This is a joint work with E. Fatighenti and D. Fiorenza. We investigate the relation between the Hodge theory of a smooth subcanonical n-dimensional projective variety X and the deformation theory of the affine cone A_X over X. We start by identifying H^{n−1,1}_{prim}(X) as a distinguished graded component of the module of first order deformations of A_X, and later on we show how to identify the whole primitive cohomology of X as a distinguished graded component of the Hochschild cohomology module of the punctured affine cone over X. In the particular case of a projective smooth hypersurface X we recover Griffiths' isomorphism between the primitive cohomology of X and certain distinguished graded components of the Milnor algebra of a polynomial defining X.

Speaker: Andreas Holmstrom (Ålesund)

Title: An elementary approach to motives

Abstract: We explain a general strategy for constructing explicit models of Grothendieck rings of Tannakian categories. Applied to categories of motives, this gives a very explicit description of various Grothendieck rings of motives, including operations such as exterior powers, symmetric powers, Adams operations, suspensions, and Tate twists. Somewhat surprisingly, it turns out that many deep statements about motives make sense in this completely elementary

framework. This project grew out of an attempt to teach motives to high-school students in Norway.

Some participants may be interested to know that the date coincides with the CAMRA Leicester Beer Festival. Some Leicester students are planning to attend the festival after the TTT and would be happy for others to join.

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.