Dr Joao Faria Martins

Profile

Some random information and links.

• 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.

• Combinatorial Representation Theory: Algebra and its interfaces with geometry, topology and combinatorics

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

• Joel Costa
• Ben Horton
• Jack Romo
• George Altmann

Projects

<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>