Dr Joao Faria Martins

Dr Joao Faria Martins


Some random information and links.


  • REF Representative. Department of Pure Mathematics, School of Mathematics
  • Former Equity, Diversity and Inclusion (EDI) Lead. School of Mathematics.

Research interests

  • algebraic and geometric topology in dimensions 3 and 4;
  • topological quantum field theories, including extended TQFTs.
  • homotopical algebra: algebraic models for homotopy types;
  • higher dimensional category theory;
  • Hopf algebras and quantum (q-deformed) Lie groups;
  • differential geometry (higher Lie and gauge theory);
  • mathematical aspects of Chern-Simons theory, BF-theory and generalisations;
  • applications to condensed matter physics and quantum computing.
<h4>Research projects</h4> <p>Any research projects I'm currently working on will be listed below. Our list of all <a href="https://eps.leeds.ac.uk/dir/research-projects">research projects</a> allows you to view and search the full list of projects in the faculty.</p>


  • PhD University of Nottingham

Student education

I am passionate about delivering an outstanding and inclusive learning experience to students of all backgrounds.
Some modules that I taught / I am teaching:

Research groups and institutes

  • Pure Mathematics

Current postgraduate researchers

<h4>Postgraduate research opportunities</h4> <p>We welcome enquiries from motivated and qualified applicants from all around the world who are interested in PhD study. Our <a href="https://phd.leeds.ac.uk">research opportunities</a> allow you to search for projects and scholarships.</p>
    <li><a href="//phd.leeds.ac.uk/project/596-algebraic,-geometric-and-physical-underpinnings-of-topological-quantum-computation">Algebraic, geometric and physical underpinnings of topological quantum computation</a></li> <li><a href="//phd.leeds.ac.uk/project/1864-combinatorial-and-higher-categorical-techniques-in-low-dimensional-topology-and-topological-quantum-field-theory">Combinatorial and higher-categorical techniques in low dimensional topology and topological quantum field theory</a></li>