Title: G2 Moduli Spaces May Have Holes
Date: Friday 2 May 2025, 12:10pm in Napier 108
Abstract: In his two seminal articles, Dominic Joyce not only constructed the first examples of closed manifolds with G2-holonomy metrics, but also proved that the moduli space of all G2-metrics on a closed manifold is itself a finite-dimensional manifold. The statement is, however, only a local one, and the global topological properties of these moduli spaces have remained quite mysterious ever since. Indeed, up to now, we only know that they may be disconnected by the work of Crowley, Goette, and Nordström; the question whether all path components are contractible or not has not been answered yet.
Title: TBA
Date: Friday 16 May 2025, 12:10pm in Lower Napier LG28 Lecture Theatre
Abstract: TBA
Title: TBA
Date: Friday 30 May 2025, 12:10pm in Lower Napier LG28
Lecture Theatre
Title: TBA
Date: Friday 13 June 2025, 12:10pm in Engineering &
Math EMG06
Title: The Holonomy Groups of Symmetric Spaces
Date: Thursday 1 May 2025, 11:10pm in Lower Napier LG28
Abstract: The Holonomy group of a Riemannian manifold is a global differential geometric invariant of the Riemannian manifold that provides information about the addition structures of the Riemannian manifold. In general it is hard to compute. However, in case of symmetric spaces, the global computation reduce to local ones, which simplifies the problem significantly.Title: G2 Moduli Spaces May Have Holes
Date: Friday 2 May 2025, 12:10pm in Napier 108
Abstract: In his two seminal articles, Dominic Joyce not only constructed the first examples of closed manifolds with G2-holonomy metrics, but also proved that the moduli space of all G2-metrics on a closed manifold is itself a finite-dimensional manifold. The statement is, however, only a local one, and the global topological properties of these moduli spaces have remained quite mysterious ever since. Indeed, up to now, we only know that they may be disconnected by the work of Crowley, Goette, and Nordström; the question whether all path components are contractible or not has not been answered yet.
Title: Holomorphic and algebraic immersed curves directed by a flexible cone
Date: Friday 4 April 2025, 12:10pm in Benham G25 Peter Martin Room
Abstract: I will describe recent joint work with Antonio Alarcon (Crelle 2025) and Alarcon and Franc Forstneric (arXiv 2024). We investigate immersed complex curves in complex affine space, directed by a cone A satisfying one of the flexibility properties that are studied in Oka theory. When A is the so-called null quadric, such curves play a fundamental role in the theory of minimal surfaces. There are other important examples. We are interested in approximation and interpolation theory for such curves, as well as the "rough shape" of the space of all curves. I will review results from 5-10 years ago in the holomorphic case and then describe our recent results in the algebraic setting, where obstacles not present in the holomorphic case arise.
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: 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