Discovery Projects - Grant ID: DP230100434

Funding Activity

Website
http://dataportal.arc.gov.au/NCGP/Web/Grant/Grant/DP230100434

Funding Status
Active

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Funded Activity Summary

A Functional Analysis of the Hypoelliptic Laplacian. Strike a bell, a sphere, or any geometrical object, and it rings. The frequencies of ringing are the mathematical spectrum, which encodes deep secrets about the shape of the object. The spectrum of the hypoelliptic laplacian is known to carry deep truths in mathematics and physics, but it remains difficult to understand. We propose a new analytic foundation, which will replace the so far non-analytical ad hoc approach, and make accessible many new results. It is key to better understanding differential equations which lie at the boundary between quantum mechanics and the classical world. This will pave the way for Australian leadership in a new century of differential equations and geometry, and training of young mathematicians.

Funded Activity Details

Start Date: 01-01-2023

End Date: 31-12-2025

Funding Scheme: Discovery Projects

Funding Amount: $415,000.00

Funder: Australian Research Council

Research Topics

ANZSRC Field of Research (FoR)

Lie groups harmonic and Fourier analysis | Operator algebras and functional analysis | Algebraic and differential geometry | Pure mathematics

ANZSRC Socio-Economic Objective (SEO)

Other Keywords

Algebraic and differential geometry | Expanding Knowledge In the Mathematical Sciences | Lie groups harmonic and Fourier analysis | Operator algebras and functional analysis | Pure mathematics

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