Emergent Physics From Lattice Models of Higher Gauge Theory
Soon to start.
Participants:
Dr João Faria Martins (PI); Prof. Paul Purdon Martin (co-I);
Dr Jiannis Pachos (member of the steering committee);
and, see advert below.
Post-doc position now open at Leeds: Closing Date:
Tuesday
29
May 2018
Research Fellow in Geometric Topology, Topological Quantum Field Theory
and Applications to Quantum Computing,
Our project aim is to investigate the different types of point-like and loop / string-like topologically excited states arising in higher gauge theory lattice models for (3+1)-dimensional topological phases of matter, categorifying Kitaev quantum double model for (2+1)-dimensional topological phases.
A central topic of this project concerns analysing the behaviour of loop excitations when they move in three-dimensional space, braid and interact, and explore applications to topological quantum computing and to knot theory in four dimensions.
Keywords:
• 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.

Some relevant previous publications:
Bullivant A, Calçada M,
Kádár Z and Martin
P , 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 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 .:
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.