Home page of João Faria Martins
Contacts:
Dr João Faria Martins,
(also known as Joao Goncalves Faria Martins)
Associate Professor (Teaching and Research)
Algebra Group,
Department of Pure Mathematics.
Equality Equity, Diversity and Inclusion Lead.
School of Mathematics,
University of Leeds,
Leeds,
LS2 9JT, UK.
E-mail:
j.fariamartins@leeds.ac.uk
Telephone: (+44) (0113) 343 5130.
My official page at the Faculty of Engineering and Physical Sciences at Leeds.
•
Conferences; •
list of publications; • compiling xymatrix diagrams into HTML using Lwarp
Lwarp with Xy-Jaxv3 (split page version) and Lwarp with Xy-Jaxv3 (stand alone page version).
My pages at
•Mathematical Reviews; • Scopus;
• Web of Science; •
scholar.google; •
inspire (hep-th);
• ORCID; • arXiv.
Participation in some grant projects of FCT (Portugal):
Research interests:
- 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):
- Torzewska
F,
Faria Martins J,
Martin
P: Motion groupoids and mapping class groupoids. arXiv:2103.10377 [math-ph]. (Updated version to appear in Communications in Mathematical Physics.)
- Faria Martins J, Porter T : A categorification of Quinn's finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from strict omega-groupoids. arXiv:2301.02491 [math.CT]. (235 pages: preprint only.)
- Damiani C, Martin
P, and Faria Martins J:
On a canonical lift of Artin's representation to loop braid groups,
Journal of Pure and Applied Algebra Volume 225, Issue 12, December 2021, 106760.
Postprint version.
- 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. Postprint version. Arxiv 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. Postprint version. Earlier version (arXiv:1702.00868 [math-ph]).
- 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.
- 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.
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.
Some selected talk videos
- Crossed modules, homotopy 2-types, knotted surfaces and welded knots. Topological Quantum Field Theory Club (Lisbon). Slides. 30/10/2020, Friday, 17:00.
- Quinn Finite Total Homotopy TQFT as a once-extended TQFT. Topological Quantum Field Theory Club (Lisbon). 24/09/2021, Friday, 17:00.
- Quinn Finite Total Homotopy TQFT as a once-extended TQFT
Geometry, Topology, and Physics (GTP) Seminar,
Center for Quantum and Topological Systems, NYU Abu Dhabi. Slides. 29/03/2023.
Some selected talk slides