A Research Project Grant, funded by the Leverhulme Trust . |

Participants:

** Post-doc position now open at Leeds: Closing Date:
Tuesday
29
May 2018 **

• TQFTs; • Extended TQFTs; • Knotted Surfaces; • Loop Braid Group and Necklace Braid Group; • 2-group; • Crossed Module; • Higher Gauge Theory; • Categorification; • Topological Quantum Computing; • Braided Fusion Category.

- Bullivant A, Martin P, and Faria Martins J: From Aharonov-Bohm type effects in discrete (3+1)-dimensional higher gauge theory to representations of the Loop Braid Group.
- 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 .
- Bullivant A, Calçada M,
Kádár Z, Martin
P, and 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.:
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 Knizhnikâ€“Zamolodchikov connection:
Lucio Simone Cirio,
*Differential Geometry and its Applications*, Volume 30, Issue 3, June 2012, Pages 238â€“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. - 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 - 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, 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. - Faria Martins J: Categorical
Groups, Knots and Knotted Surfaces,
*J. Knot Theory Ramifications*16 (2007), no 9, 1181-1217.