Title: Topology dictates the algebra: an intro to TQFT
Date: Thursday 20 March 2025, 11:10am in Lower Napier LG28
Abstract: Topological quantum field theories originate in interactions between physics and mathematics that began in the 1980s. We give a gentle introduction to them, show how low dimensional examples give rise to natural algebraic structures, and what more extended classification results look like.Title: Poincaré duality for families of supermanifolds
Date: Friday 21 March 2025, 12:10pm in Napier 108
Abstract: It is well known to experts, but seldom discussed explicitly, that smooth supergeometry is best done in families. This is also called the relative setting, and it implies that we need relative versions of standard supergeometric constructions. Such constructions include the de Rham complex familiar from ordinary differential geometry, but in the supergeometric setting, they also include more exotic objects, such as the Berezinian line bundle (whose sections are the correct objects to integrate over supermanifolds) and the related complex of integral forms, where the super version of Stokes' theorem lives. To work in families, we introduce relative versions of the de Rham complex and the integral form complex, and we prove that they satisfy a relative version of Poincaré duality. No background in supergeometry will be assumed for this talk.
Title: TBA
Date: Thursday 1 May 2025, 11:10pm in Lower Napier LG28
Abstract: TBATitle: TBA
Date: Friday 2 May 2025, 12:10pm in Napier 108
Abstract: TBA
Title: TBA
Date: Friday 30 May 2025, 12:10pm in Lower Napier LG28
Lecture Theatre
Title: Computing shortest curves on surfaces
Date: Tuesday 4 March 2025, 11:10am in Engineering & Math EMG06
Abstract: The task at hand is to compute a shortest loop that cannot be contracted to