Elliptic special functions. Although elliptic functions and special functions are both classical areas of mathematics, the field of elliptic special functions was only established in the last two decades. It combines ideas from analysis, modular forms and statistical mechanics to tackle problems in number theory (elliptic curves), algebra (elliptic quantum groups), mathematical physics (Seiberg duality) and more. This project aims to settle two important problems in the field of elliptic special ....Elliptic special functions. Although elliptic functions and special functions are both classical areas of mathematics, the field of elliptic special functions was only established in the last two decades. It combines ideas from analysis, modular forms and statistical mechanics to tackle problems in number theory (elliptic curves), algebra (elliptic quantum groups), mathematical physics (Seiberg duality) and more. This project aims to settle two important problems in the field of elliptic special functions: the resolution of Boyd's conjectures concerning Mahler measures and L-values of elliptic curves, and the construction of an Askey-Wilson-Koorwinder theory of elliptic biorthogonal functions for the A-type root system.Read moreRead less
Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contri ....Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contributions to these topics: Regularity problem and energy minimality of weakly harmonic maps, Weak solutions of the liquid crystal equilibrium system, Yang-Mills heat flow and singular Yang-Mills connections.
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Population-level Epidemiological Trends In Hepatocellular Carcinoma In Queensland 1996 - 2010.
Funder
National Health and Medical Research Council
Funding Amount
$251,695.00
Summary
Incidence and mortality of hepatocellular carcinoma (HCC, the most common form of liver cancer) is increasing in Australia, driven by viral hepatitis infections. Disease burden is not defined in Queensland, particularly for Indigenous, migrant and regional and remote communities. Such factors may influence risk of viral hepatitis, access to treatment, and incidence and survival of HCC. Defining disease burdens will enable clinical programs targeted at groups most at risk in order to impact HCC t ....Incidence and mortality of hepatocellular carcinoma (HCC, the most common form of liver cancer) is increasing in Australia, driven by viral hepatitis infections. Disease burden is not defined in Queensland, particularly for Indigenous, migrant and regional and remote communities. Such factors may influence risk of viral hepatitis, access to treatment, and incidence and survival of HCC. Defining disease burdens will enable clinical programs targeted at groups most at risk in order to impact HCC trends.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE110100023
Funder
Australian Research Council
Funding Amount
$500,000.00
Summary
Integrated command and control facility for large-scale critical infrastructure management. This is a test bed facility for achieving sustainable operation of Australia's critical infrastructure, particularly at airports. The facility will enable an integrated and coordinated strategy to increase operational resilience while not losing sight of the complex nature and dynamic requirements of critical infrastructure management.