Projects per year
Personal profile
Research interests
The questions I am interested in mix geometry with partial differential equations.
Geometric evolution equations: here we deform geometric objects in a smooth way to help us understand their shape. This is a very powerful recent technique in geometric analysis, and has been crucial in solving many open geometric questions, including the Poincare conjecture (proved by Perelman).
Eigenvalue estimates: Every geometric object has a set of numbers attached to it, called the spectrum. These are like the resonant frequencies of a drum. I am interested in how the shape of the object affects the spectrum.
Capillary surfaces and the calculus of variations: Consider a meniscus--- the interface between the water in a glass and the air above it. The special shape of the meniscus is due to an interplay between the energy used in the water/glass interface and the air/water interface, and the gravitational energy--- the shape we see will minimise the sum of these energies. It will also dependent on the shape of the glass and the volume of the water. This is a typical problem in the calculus of variations, where minimizing a physical quantity can give rise to interesting geometric shapes.
Monash teaching commitment
Second semester 2017:
M41022 Partial Differential Equations
MTH3160 Functional Analysis
Second semester 2018
MTH3160 Metric spaces, Banach spaces, Hilbert spaces
Research area keywords
- eigenvalues
- parabolic equations
- heat flow
- geometric analysis
- calculus of variations
- geometric evolution equations
- mean curvature flow
- spectral theory
Network
Projects
- 1 Finished
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Curvature flows and spectral estimates.
Australian Research Council (ARC)
1/04/14 → 31/12/20
Project: Research
Research output
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The maximum flux of star-forming galaxies
Crocker, R. M., Krumholz, M. R., Thompson, T. A. & Clutterbuck, J., 21 Jul 2018, In : Monthly Notices of the Royal Astronomical Society. 478, 1, p. 81-94 14 p.Research output: Contribution to journal › Article › Research › peer-review
Open AccessFile10 Citations (Scopus) -
Non-concavity of Robin eigenfunctions
Clutterbuck, J. F., Hauer, D. & Andrews, B., 8 Nov 2017, 48 p.Research output: Working paper › Working Paper › Other
File -
Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue
Andrews, B. & Clutterbuck, J. F., 2013, In : Analysis & PDE. 6, 5, p. 1013 - 1024 12 p.Research output: Contribution to journal › Article › Research › peer-review
20 Citations (Scopus) -
Proof of the fundamental gap conjecture
Andrews, B. & Clutterbuck, J. F., 2011, In : Journal of the American Mathematical Society. 24, 3, p. 899 - 916 18 p.Research output: Contribution to journal › Article › Research › peer-review
58 Citations (Scopus) -
Stability of mean convex cones under mean curvature flow
Clutterbuck, J. F. & Schnurer, O. C., 2011, In : Mathematische Zeitschrift. 267, 3-4, p. 535 - 547 13 p.Research output: Contribution to journal › Article › Research › peer-review
3 Citations (Scopus)
Prizes
Activities
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Scientific director, AMSI Winter School
Julie Clutterbuck (Chair/ Co-Chair)
2 Jul 2018 → 13 Jul 2018Activity: External Academic Engagement › External research and teaching
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Joint PDE and Geometric Analysis Meeting: Australian National University, Pacific Institute of Mathematical Sciences, Beijing International Centre for Mathematical Research
Julie Clutterbuck (Organiser)
5 Feb 2018Activity: Participating in or organising an event types › Contribution to conference
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Workshop
Julie Clutterbuck (Organiser)
16 Oct 2017 → 28 Oct 2017Activity: Participating in or organising an event types › Contribution to conference
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New Zealand MathematicalSociety Colloquium
Julie Clutterbuck (Keynote/plenary speaker)
5 Dec 2017 → 7 Dec 2017Activity: Participating in or organising an event types › Contribution to conference