Differential Geometry Seminars 2024
- Date: Fri, 15 Mar - Tue, 31 Dec 2024
- Location: Engineering North N218, North Terrace Campus
- Contact: Thomas Leistner +61 8 8313 6401
- Email: thomas.leistner@adelaide.edu.au
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.
All seminars will be held on a Friday, From 12:10pm till 1:00pm. Seminars will be held in Engineering North N218.
Date | Speaker | Presentation |
---|---|---|
15 March 2024 |
Finnur Lárusson |
Reconciling dichotomies in holomorphic dynamics I will describe recent joint work with Leandro Arosio (University of Rome, Tor Vergata) in holomorphic dynamics. We study the iteration of endomorphisms of complex manifolds of a fairly general kind, as well as the iteration of automorphisms for a class that is somewhat smaller, but still includes almost all linear algebraic groups. The main goal of our work is to reconcile two fundamental dynamical dichotomies in these settings, "attracted vs. recurrent" and "calm vs. wild". |
27 March 2024 3:10pm Lower Napier LG18 |
Radboud University |
A higher index theorem on finite-volume locally symmetric spaces Let G be a (connected, real, semisimple, real rank one) Lie group, and K a maximal compact subgroup. Let Gamma be a torsion-free, discrete subgroup of G. If the double-coset space X = Gamma\G/K is compact, then we can do index theory on it, both in the classical Atiyah-Singer sense and in the sense of higher index theory with values in the K-theory of the C*-algebra of Gamma. But in many relevant cases, X has finite volume, but is noncompact. This includes the case where G = SL(2,R), K = SO(2) and Gamma = SL(2,Z). Then Moscovici constructed an index of Dirac operators on X, and Barbasch and Moscovici computed it using the (Arthur-)Selberg trace formula. In ongoing work with Hao Guo and Hang Wang, we upgrade this to a higher index with values in a relevant K-theory group. This talk is a relatively gentle introduction, focusing mainly on the classical case. |
5 April 2024 12:10pm Engineering North N218 |
University of Cambridge |
Global Stability of Spacetimes with Supersymmetric Compactifications Compact spaces with special holonomy, such as Calabi-Yau manifolds, play an important role in supergravity and string theory. In this talk, I will present a recent result showing the stability of a spacetime which is the cartesian product of Minkowski spacetime and a compact special holonomy space. I will also explain how this stability result relates to conjectures of Penrose and Witten. This is based on joint work with L. Andersson, P. Blue and S-T. Yau. |
3 May 2024 12:10pm Engineering North N218 |
University of Adelaide |
Killing tensors on complex projective space The Killing tensors on the round sphere are well understood. In particular, these are finite-dimensional vector spaces with very nice formulae for their dimensions. What about the corresponding story for complex projective space? Again, these are finite-dimensional spaces and their dimensions can be computed. Formulae for their dimensions, however, are simultaneously nice but seriously puzzling! If time permits: what about quaternionic projective space and so on? Some of this was discussed in my TOPS series last September but I’ll start again from scratch and, in particular, explain what are Killing tensors and why they are useful. |