- Lecturer in Algebra

School of Mathematics,

University of Leeds,

Leeds, LS2 9JT, UK.

- E-mail:
j.fariamartins@leeds.ac.uk

Telephone: (+44) (0113) 343 5130.

** Soon to come: **

• Conferences, • mini-CV, • list of publications, • outreach.

My pages at

•Mathematical Reviews, • Scopus, • ResearcherID, • scholar.google, • inspire (hep-th), • ORCID, • arXiv.

- algebraic and geometric topology in dimensions 3 and 4;
- algebraic models for homotopy types;
- higher dimensional category theory;
- homotopical algebra;
- 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;
- mathematical models for topological phases of matter;
- topological quantum computing.

- Bullivant A, Calçada M, Kádár Z and Martin P, Faria Martins J: Topological phases from higher gauge symmetry in 3+1 dimensions. PHYSICAL REVIEW B 95, 155118 (2017). Preliminary version.
- Cirio L.S., Faria Martins J. Categorifying the $sl(2,C)$ Knizhnik-Zamolodchikov Connection via an Infinitesimal 2-Yang-Baxter Operator in the String Lie-2-Algebra. Advances in Theoretical and Mathematical Physics. Volume 21 (2017) Number 1, Pages: 147 - 229 Preliminary version.
- Faria Martins J.: Crossed modules of Hopf algebras and of associative algebras and two-dimensional holonomy. Journal of Geometry and Physics Volume 99, January 2016, Pages 68-110. Preliminary version.
- Cirio L.S, Faria Martins J.: Infinitesimal 2-braidings and differential crossed modules, Advances in Mathematics, Volume 277, 4 June 2015, Pages 426-491. Preliminary version.
- Gohla B.; Faria Martins J.: Pointed homotopy and pointed lax homotopy of 2-crossed module maps, Advances in Mathematics Volume 248, 25 November 2013, Pages 986-1049. Preliminary version. Very preliminary version.
- Faria Martins J, Mikovic A. :Lie crossed modules and
gauge-invariant actions for 2-BF theories,
*Advances in Theoretical and Mathematical Physics*, Volume 15, Number 4 (August 2011) p.1059-1084. Preliminary version - Faria Martins J, Picken R..: Surface
Holonomy for Non-Abelian 2-Bundles via Double Groupoids,
*Advances in Mathematics Volume 226, Issue 4, 1 March 2011, Pages 3309-3366. Preliminary version. Very preliminary version.* *Faria Martins J, Picken R..:*The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module, Differential Geometry and its Applications Volume 29, Issue 2, March 2011, Pages 179-206. Preliminary version. Very preliminary version.- Faria Martins J., Picken R..On
Two-Dimensional Holonomy,
*Transactions of the American Mathematical Society*, 362 (2010), 5657-5695. - Faria Martins J.: The
Fundamental Crossed Module of the Complement of a Knotted Surface.
*Transactions of the American Mathematical Society.*361 (2009), 4593-4630. - Faria Martins J., Kauffman L.H.:
Invariants of Welded Virtual Knots Via Crossed Module Invariants of Knotted Surfaces, Compositio Mathematica. Volume 144, Issue 04, July 2008, pp 1046-1080. - Faria Martins J, Mikovic A.: Invariants
of Spin Networks Embedded in Three-Manifolds,
*Communications in Mathematical Physics,*Volume 279, Number 2/ Abril 2008, pages 381-399.

- Faria Martins J, Porter T : On
Yetter's Invariant and an Extension of the Dijkgraaf-Witten Invariant
to Categorical Groups,
*Theory and Application of Categories,*Vol. 18, 2007, No. 4, pp 118-150.