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2023 Differential Geometry Seminars

School of Mathematical Sciences – The University of Adelaide.

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Differential Geometry Seminar: Reconciling dichotomies in holomorphic dynamics

I will describe recent joint work with Leandro Arosio (University of Rome, Tor Vergata) in holomorphic dynamics.

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Differential Geometry Seminar: 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.

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Differential Geometry Seminar: 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.

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Differential Geometry Seminar: 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.

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Differential Geometry Seminar: Killing tensors on symmetric spaces

I will present some recent results on the structure of the algebra of Killing tensors on Riemannian symmetric spaces. The fundamental question is whether any Killing tensor field on a Riemannian symmetric space is a polynomial in (a symmetric product of) Killing vector fields.

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Differential Geometry Seminar: Nearly Kähler geometry and totally geodesic submanifolds

A theorem of Butruille asserts that the (simply connected, homogeneous) Riemannian manifolds of dimension six admitting a strict nearly Kähler metric are the round sphere S6, the space F(C3) of full flags in C3, the complex projective space CP3 and the almost product S3 x S3.

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Workshop: Australia-China-Japan-Singapore-U.S. Index Theory

Goodman Crescent

This is the third edition of a series of international conferences on Index Theory. This year, it will be held at the University of Adelaide, Adelaide, Australia.

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Differential Geometry Seminar: An application of elliptic cohomology to quantum groups

I will start by reviewing quantum groups (including quantum groups at roots of unity, Yangians, etc) and their representation theory. I will then explain the construction of quantum groups using cohomology theories from topology.

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Differential Geometry Seminar: Boundedness problems in algebraic geometry and their consequences

In 1960’s Shafarevich asked a simple question: Do families of curves of genus at least 2 (over a fixed base) have finite number of deformation classes?

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