~ Next talks ~

• John Huerta (University of Lisbon/ANU)

  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.
  This is joint work with Konstantin Eder and Simone Noja.