Dr Joao Faria Martins
- Position: Associate Professor (Teaching and Research). Department of Pure
- Areas of expertise: (Extended) TQFTs; higher gauge theory; higher category theory; homotopical algebra; quantum invariants of knots and manifolds; topological quantum computing; modelling topological phases of matter.
- Email: J.FariaMartins@leeds.ac.uk
- Phone: +44(0)113 343 4433
- Location: 9.22 School of Mathematics
- Website: Personal homepage | MathSciNet | Googlescholar | ORCID
Profile
Some random information and links.
- List of publications.
- PhD: University of Nottingham, 2004. In Leeds since 2016.
- Yorkshire and Midlands Category Theory Seminar: a category theory research network between the universities of Leeds, Manchester and Sheffield. The network is partially funded by the London Mathematical Society.
- Compiling xymatrix diagrams into HTML using Lwarp and Lwarp with Xy-Jaxv3: Check this link for instructions on how to compile latex into accessible HTML, using Lwarp, a TeX Live package, with minor tweaks so that xymatrix diagrams are displayed using Xy-Jaxv3.
- Conferences co-organised by João Faria Martins: Check this link for conferences, past, present and future.
- the Leverhulme Trust Research Project Grant (PI): Emerging Physics From Lattice Models of Higher Gauge Theory. (Completed.)
- Programme Grant (EPSRC): (Co-I): Combinatorial Representation Theory: Discovering the Interfaces of Algebra with Geometry and Topology, 2022-2027.
Responsibilities
- 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.
Qualifications
- 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:
- MATH3071: Groups and Symmetry,
- MATH5071: Groups, Symmetry and Galois Theory,
- MATH3017: Calculus in the Complex Plane,
- MATH3225: Topology (current).
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>Projects
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<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>