About

The AGQ Centre for Doctoral Training is a collaborative initiative between Heriot-Watt University, the University of Edinburgh, and the University of Glasgow. Our focus is on advanced training and research in Algebra, Geometry, and Quantum Fields.  Our ambition is to train the next generation of scientific leaders in academia, industry and wider society.

Vision

Mathematics research today is rapidly transforming, becoming more and more inter-connected.  Through this evolution, many classical interactions have been turned on their head. Whereas traditionally algebra served largely as the symbolic language to encode geometric intuition, today that very same intuition has given rise to a compellingly diverse range of novel algebraic structures. Simultaneously, whilst mathematics has for centuries served as the rigorous language of physics, concepts at the heart of quantum physics have recently flooded back into pure mathematics, leading to astonishing and wholly mathematical predictions, new structures, and diverse connections.

Examples of this revolution include the discovery of quantum topology and higher algebra, the advent of non-commutative geometry and geometric group theory, and diverse predictions of mirror symmetry in algebraic and symplectic geometry, to name just a few at the centre of our research.

Equally profound has been the surging impact of advanced computing – computer algebra, machine learning, artificial intelligence, and proof assistants.  This has impacted both the goals and wider ambitions, as well as the day to day practice, of mathematics research.  These developments have in turn brought theoretical mathematics – and theoretical mathematicians – to the forefront of technological changes felt throughout society, through developments in cryptography, quantum computing, and machine learning & AI, through mathematicians’ contributions in the energy, finance, and technology sectors, and finally through their engagements with education and public policy.

Our vision for this centre is two-pronged. Our students will learn to navigate the vibrant new interfaces between Algebra, Geometry, and Quantum Fields and will build a strong abstract foundation. But they will also be prepared to become leaders in industry and society, equipped with innovative problem-solving skills, with expertise in advanced computing, and with the confidence and capability to communicate their work to the wider world.

Programme

Our aim is to attract a diverse cohort of students and empower them with a range of expertise and ambition. We offer:

 

Core and contextualised scientific training in Algebra, Geometry, and Quantum Fields, and their interfaces.
Cutting edge thesis projects within and between our areas of Algebra, Geometry and Quantum Fields, delivered through our internationally esteemed and collaborative pool of 60+ supervisors.
Advanced computing training in areas such as machine learning, symbolic computing, and AI-assisted proofs.
Bespoke professional skills training in communication and networking, ethics and EDI.
Placement opportunities with one of our 30+ partners in international academia, industry, and the third-sector.

 

See our Training page for a detailed description of what our current students are learning.

Study at one of three leading UK institutions

  • Heriot-Watt University

    Heriot-Watt University is valued for its pioneering research, informed by the global needs of business and industry. With a rich heritage stretching back to 1821, it is a truly global university bringing together scholars who are leaders in ideas and solutions delivering innovation, educational excellence and ground-breaking research.

  • University of Edinburgh

    Founded in 1583, the University of Edinburgh is one of the world’s top universities. The university’s entrepreneurial and cross-disciplinary culture attracts students and staff from across the globe, and provides a stimulating working, learning and teaching environment with access to excellent facilities. Edinburgh attract the world’s best, from Nobel Prize winning laureates to future explorers, pioneers and inventors.

  • University of Glasgow

    Founded in 1451, the University of Glasgow is a major research-led university operating in an international context. It is a Top 100 university, one of the oldest universities in the United Kingdom, and the largest science based university in the UK outside of London.