Home page of João Faria Martins
Postdoctoral position at Leeds (closing date Wednesday 10 June 2020) :
Workshop recently finished:
Online thematic period going on now
Participation in some grant projects of FCT (Portugal):
- algebraic and geometric topology in dimensions 3 and 4;
- extended Topological Quantum Field Theories;
- 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.
Main scientific publications (a full list of publications is here):
- Bullivant A, Martin
P, and Faria Martins J:
Representations of the Loop Braid Group and Aharonov-Bohm like effects in discrete (3+1)-dimensional higher gauge theory. Advances in Theoretical and Mathematical Physics, Volume 23 (2019)
Number 7, Pages: 1685--1769. Preliminary version arXiv:1807.09551 [math-ph].
- Bullivant A, Calçada M, Kádár Z, Martin P, and Faria Martins J: Higher lattices, discrete two-dimensional holonomy and topological phases in (3+1) D with higher gauge symmetry. Reviews in Mathematical Physics, Vol. 32, No. 04, 2050011 (2020) | Research Paper. Preliminary version.
- 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
- 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.
- Cirio L.S, Faria Martins J.:
Categorifying the Knizhnik–Zamolodchikov connection:
Lucio Simone Cirio, Differential Geometry and its Applications, Volume 30, Issue 3, June 2012, Pages 238–261. 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.
- Faria Martins J, Picken R..: Surface
Holonomy for Non-Abelian 2-Bundles via Double Groupoids,
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
Mathematica. Volume 144, Issue 04, July 2008, pp
- 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.
Some selected talk slides