Colluqium : PreSemester Workshop on Applications of Differential Geometry 
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There are four talks this week, reporting on applications of differential geometry to nonlinear problems in dynamics, interpolation, and problems of interpolating rigid body motion. Following each talk there will be a short discussion on topics of general interest. The speakers are (note that Shreya's time has been switched with Phil's)
Shreya Bhattarai, UWA Maths
Maths LR 2 Wednesday February 23, 3:00pm
Prof. Wayne Lawton, NUS Maths and UWA Adjunct Maths LR2 Wednesday February 23, 4:00pm
Philip Schrader, UWA Maths
Maths LR2 Thursday February 24, 3:00pm
Michael Pauley, UWA Maths
Maths LR2 Thursday February 24, 4:00pm.
Abstracts for the four talks are given below.

Introduction to Conditional Extremals

Shreya Bhattarai (UWA)
Maths LR2 Wednesday February 23, 3:00pm
Conditional extremals arise as solutions to a certain variational problem on Riemannian manifolds for which there is an underlying "prior vector field"
A. When A is the zero field, conditional extremals are simply geodesics.
For
geodesics, we can talk about Jacobi fields and conjugate points and we can extend these ideas to conditional extremals as well. In this talk, I will be giving a brief introduction to conditional extremals and then discussing results and observations about their conjugate points

Periodicity and Recurrence

Wayne Lawton (NUS and UWA)
Maths LR2 Wednesday February 23, 4:00pm
Abstract: Fourier's observation that
periodic functions admit approximation
by trigonometric series led him to
construct foundations for the digital age.
This approximation occurs because trigonometric series admit arbitrary localisation within their period interval. What happens when the set of frequencies are restricted? We show how this question is related to recurrence phenomena in dynamical systems studied by Poincare, Birkhoff, Morse, and others.

Conditional Extremals and Global Analysis

Philip Schrader (UWA)
Maths LR2 Thursday February 24, 3:00pm
We define conditional extremal curves on a Riemannian manifold $M$ as the critical points of the the $L^{2}$ distance between the tangent vector field and a `prior'
vector field. The natural setting for proving necessary and sufficient conditions for existence of these curves is critical point theory on Hilbert manifolds of curves. I will briefly describe these manifolds and show how the geometry developed by Eliasson for such manifolds can be used to calculate the EulerLagrange equation and Hessian of this $L^{2}$ distance. I will also show that this distance satisfies a substitute for compactness known as the PalaisSmale condition, thus establishing the existence of critical points. If time permits, I will present a Morseindex theorem and some results on multiplicity of critical points.

Cubics and Negative Curvature

Michael Pauley (UWA)
Maths LR2 Thursday February 24, 4:00pm
Abstract: Riemannian cubics are curves that generalise cubic polynomials to arbitrary Riemannian manifolds, in the same way that geodesics generalise straight lines. In any complete Riemannian manifold, geodesics can be extended indefinitely. In this talk I will discuss the question of whether Riemannian cubics can be extended indefinitely. The sectional curvature of the manifold plays a role. Assumed knowledge:
definition of smooth manifolds, smooth maps and vector fields.

Convener,
Lyle Noakes 3358
Location 
MLR2  Maths Lecture Room 2


Contact 
Lyle Noakes
<[email protected]>
: 6488 3358

Start 
Wed, 23 Feb 2011 15:00

End 
Thu, 24 Feb 2011 17:00

Submitted by 
Susan <[email protected]>

Last Updated 
Tue, 22 Feb 2011 14:23

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