DrLinden Disney-Hogg

My research broadly falls under the umbrella of Wigner's "unreasonable effectiveness of mathematics in the natural sciences", especially the role of symmetry in specifying structure. 

 *) Computational approaches to biology have had a transformational impact upon the field in recent decades and my research has involved applications of these to achieve practical insight. I am especially interested in how the underlying mathematical structure of algorithms and data should be employed to guide development of such tools. When working with cancer datasets such considerations are especially salient. 

*) Topological solitons such as magnetic monopoles, vortices, and skyrmions arose historically from considerations in theoretical physics but their moden study utilises topology, algebraic geometry and representation theory synthesised with computational tools.  I have worked to find symmetric solitons and to describe soliton moduli by combining these approaches. 

*) Integrable systems are another topic arising from physics where algebraic geometry is a powerful tool, particularly via the role spectral curves and their theta functions play. I have sought to elucidate these structures both by developing code (for example in SageMath) to explicitly calculate their properties and leveraged this into proof. 

In all these areas where data and computation can be leveraged, I am additionally exploring how concepts and techniques from machine learning can be integrated to enhance understanding and performance.