Differential Geometry Seminars 2025
Visitors of the Institute for Geometry and its Applications and researchers from the School of Computer and Mathematical Sciences present cutting-edge research in geometry and other areas of pure mathematics.
Date | Speaker | Presentation |
---|---|---|
Tuesday |
Stephan Tillmann |
Computing shortest curves on surfaces The task at hand is to compute a shortest loop that cannot be contracted to |
Thursday 20 March 2025 11:10 am Napier LG28 |
John Huerta University of Lisbon/ANU |
Topology dictates the algebra: an intro to TQFT 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. |
Friday |
John Huerta |
Poincaré duality for families of supermanifolds 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. |
Friday 4 April 2025 12:10 pm Benham G25 Peter Martin Room |
Finnur Larusson University of Adelaide |
Holomorphic and algebraic immersed curves directed by a flexible cone 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. |
Friday |
Thorsten Hertl University of Melbourne |
TBA Note: Thorsten will also give an introductory talk on Thursday 1 May 2025, 11:10 am in Lower Napier LG28 |
Friday 30 May 2025 12:10 pm Lower Napier LG28 Lecture Theatre |
Arumina Ray University of Melbourne |
TBA |