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Jesse Gell-Redman (University of Melbourne)
Yuri Nikolayevsky (La Trobe University)
Nadezda Sukhorukova (Swinburne University)
| Time | Speaker/Event |
|---|---|
| 11:00 | Nadezda Sukhorukova |
| 12:00 | Lunch |
| 13:30 | Jesse Gell-Redman |
| 14:30 | Afternoon Tea |
| 15:00 | Yuri Nikolayevsky |
Speaker: Nadezda Sukhorukova, Department of Mathematics, Swinburne University of Technology.
Title: About the Extremal Principle: From Convex Analysis to Nonsmooth Analysis (Geometric Considerations)
Abstract: In this talk, I will formulate a number of optimality conditions appearing in non-smooth optimisation and approximation problems. Most of these conditions can be formulated in terms of convex polytopes. This geometrical interpretation of optimality gives rise to beautiful mathematical theories as well as computational methods. Most example of this talk are coming from polynomial and piecewise polynomial approximation (classical results) and approximation by neural networks (current research).
Speaker: Jesse Gell-Redman, School of Mathematics and Statistics, University of Melbourne
Title: The Feynman propagator for the Klein-Gordon equation
Abstract: We construct the Feynman propagator for Klein-Gordon (KG) equation on Minkowski space perturbed by a decaying spatial potential. In particular, we construct global in time solutions to the inhomogeneous KG equation, each of whose wavefront sets is contained in the flowout of the wavefront set of the source in the direction of the Hamilton flow. Such solutions were shown to exist locally by Duistermaat-Hörmander. To accomplish this, we prove a global Fredholm estimate. The persistence of the potential in time means that estimates for KG can be obtained using positive commutator estimates with operators in the three-body calculus of Vasy. This is joint work with Dean Baskin and Moritz Doll.
Speaker: Yuri Nikolayevsky, Mathematics and Statistics, La Trobe University
Title: Killing tensors on symmetric spaces
Abstract: 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. For spaces of constant curvature, the answer is in the positive (as has been known for quite some time). The same is true for the complex projective space (Eastwood, 2023). Surprisingly, for other rank one symmetric spaces (quaternionic projective space and Cayley projective plane), the answer is almost always in the negative (Matveev-Nikolayevsky, 2024). If time permits we’ll also discuss quadratic Killing tensors on higher rank spaces and some very recent results on rank-one spaces. This is a joint project with V.Matveev (University of Jena, Germany), O.Dearricott and An Ky Nguyen (both from La Trobe).