Roger Picken

email: roger.picken@tecnico.ulisboa.pt

Associate Professor at the Mathematics Department of Instituto Superior Técnico (IST), Lisbon.

Member of the research centre CAMGSD and co-organizer of the Topological Quantum Field Theory Club.

Main Research Interests

Topological quantum field theory (TQFT); geometry of abelian and nonabelian n-gerbes with connection, and higher gauge theory;
quantum gravity in (2+1) space-time dimensions; knot theory

Teaching

Current teaching

Supervision

Road to Persistence, Tomás Carrondo
Undergraduate project, July 2021

The Eisermann invariant of long knots via braids, João Tavares
Undergraduate project, July 2020

Exploratory Topological Data Analysis of Resting-State fMRI Data, Marta Castro
MSc thesis, December 2019

Anyons and Topological Quantum Computation, João Oliveira
Undergraduate project, July 2018

Mathematics and Scottish Country Dance, Maria Eusébio
Undergraduate project, July 2018

The lifting of the Eisermann invariant - some results, Sofia Brito
Undergraduate project, September 2016

Group and 2-group presentations, Luís Duarte
Gulbenkian New Talents in Mathematics programme, September 2015

Quotient 2-groups and the Postnikov decomposition, Miguel Martins dos Santos
Gulbenkian New Talents in Mathematics programme, September 2014

A new class of 2-D TQFT from finite 2-groups, Diogo Bragança
Gulbenkian New Talents in Mathematics programme, September 2013

Odd Khovanov homology for virtual knots, Diana Tavares
Master's thesis (co-supervised with Marco Mackaay), April 2010

Welded Braids and the Crossed Module Invariant, Marta Carreteiro
Master's thesis (co-supervised with João Faria Martins and F. Miguel Dionísio), September 2009

A Combinatorial Approach to the HOMFLY n-Specializations, Nuno Freitas
Master's thesis, June 2008

Será possível encontrar topologia numa fábrica? Daniela Pontes
Gulbenkian New Talents in Mathematics programme, March 2006

Publications and preprints

2-group actions and moduli spaces of higher gauge theory
By Jeffrey C.Morton, Roger Picken. J. Geom. Phys. 148, February 2020, 103548.
e-Print Archive: 1904.10865

Some properties of Bowlin and Brin's color graphs
By Rui Pedro Carpentier, Roger Picken. Discrete Mathematics 343 (1), January 2020, 11163.
e-Print Archive: 1804.08397

Quantum holonomies and the Heisenberg group
By J. E. Nelson, R. F. Picken. Modern Physics Letters A 34 (31), (2019), 195025
e-Print Archive: 1808.08812

Invariants and TQFT's for cut cellular surfaces from finite 2-groups
By Diogo Bragança, Roger Picken. Bol. Soc. Port. Mat. 76 (2019) 159-176.
e-Print Archive: 1710.02390

Invariants and TQFT's for cut cellular surfaces from finite groups
By Diogo Bragança, Roger Picken. Bol. Soc. Port. Mat. 74, 17-44 (2016).
e-Print Archive: 1512.08263

Transformation Double Categories Associated to 2-Group Actions
By Jeffrey C. Morton, Roger Picken. Theory Appl. Categ. 30, Paper No. 43, 1429-1468 (2015).
e-Print Archive: 1401.0149

Theory of intersecting loops on a torus
By J. E. Nelson, R. F. Picken. Adv. Theor. Math. Phys, 18 (3), (2014) 709–740.
e-Print Archive: 1309.2187

Colourings and the Alexander Polynomial
By Luís Camacho, F. Miguel Dionísio, Roger Picken. Kyungpook Mathematical Journal, 56 (3) 1017-1045 (2016).
e-Print Archive: 1303.5019

Link invariants from finite categorical groups
By João Faria Martins and Roger Picken. Homology, Homotopy and Applications, 17 (2) 205-233 (2015)
e-Print Archive: 1612.03501
Se also: e-Print Archive: 1301.3803

On invariants of almost symplectic connections
By Rui Albuquerque and Roger Picken. Math. Phys. Anal. Geom. 18 (2015), no. 1, Art. 8, 13 pp.
e-Print Archive: 1107.1860

Quantum geometry from 2+1 AdS quantum gravity on the torus
By J. E. Nelson, R. F. Picken. Gen. Relativity Gravitation, 43(3):777-795, 2010.
e-Print Archive: 1006.0921

The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module
By Joao Faria Martins, Roger Picken. Differential Geom. Appl. 29 (2011), no. 2, 179–206.
e-Print Archive: 0907.2566

Surface Holonomy for Non-Abelian 2-Bundles via Double Groupoids
By Joao Faria Martins, Roger Picken. Adv. Math. 226 (2011), no. 4, 3309–3366.
e-Print Archive: 0808.3964

A quantum Goldman bracket in 2+1 quantum gravity
By J. E. Nelson, R. F. Picken . J. Phys. A 41:304011, 2008
e-Print Archive: 0711.2271

On two-Dimensional Holonomy
By Joao Faria Martins, Roger Picken. Trans. Amer. Math. Soc., 362 (2010), 5657-5695
e-Print Archive: 0710.4310

Constant connections, quantum holonomies and the Goldman bracket
By J. E. Nelson, R. F. Picken. Adv. Theor. Math. Phys. 9 (2005) 407-433
e-Print Archive: math-ph/0412007

Parasupersymmetric Quantum Mechanics of Order 3 and a Generalized Witten Index
By Marko Stosic, Roger Picken. Mod. Phys. Lett. A 20, No. 17-18, 1395-1407 (2005).
e-Print Archive: math-ph/0407019

A cohomological description of Abelian bundles and gerbes
By Roger Picken. In "Twenty Years of Bialowieza: A mathematical Anthology. Aspects of Differential Geometric Methods in Physics", S.T. Ali et. al. Eds., World Scientific, Singapore (2005).
e-Print Archive: math/0305147

TQFT'S AND GERBES.
By Roger Picken. Feb 2003. 21pp. Published in Algebraic and Geometric Topology, Volume 4 (2004) paper no. 14, 243-272.
e-Print Archive: math.dg/0302065

A CLASSICAL APPROACH TO TQFT'S.
By R.F. Picken, P.A. Semiao. Dec 2002. 72pp.
e-Print Archive: math.qa/0212310

PARAMETRIZATION OF THE MODULI SPACE OF FLAT SL(2,R) CONNECTIONS ON THE TORUS.
By J.E. Nelson (Turin U. & INFN, Turin), R.F. Picken (Lisbon, IST). DFTT-12-2001, IST-DM-20-01, May 2001. 12pp.
Published in Lett.Math.Phys.59:215-226,2002
e-Print Archive: math-ph/0105015

THE HOLONOMY OF GERBES WITH CONNECTIONS.

By Marco Mackaay (Algarve U.), Roger Picken (Lisbon, IST). Sep 2000. 49pp.
Published in Adv. Math. 170:287-339, 2002 e-Print Archive: math.dg/0007053

SUPER CHERN SIMONS THEORY AND FLAT SUPER CONNECTIONS ON A TORUS.
By A. Mikovic, R. Picken (Lisbon, IST). IST-DM-16-00, Aug 2000. 16pp.
Published in Adv.Theor.Math.Phys.5:243-263,2002
e-Print Archive: math-ph/0008006

TQFT: A NEW DIRECTION IN ALGEBRAIC TOPOLOGY.
By R.F. Picken (Lisbon, IST), P.A. Semiao (Algarve U.). IST-DM-36-99, Dec 1999. 16pp.
Contributed to Workshop on New Developments in Algebraic Topology, Faro, Portugal, 13-15 Jul 1998.
e-Print Archive: math.qa/9912085

QUANTUM MATRIX PAIRS.
By J.E. Nelson (Turin U.), R.F. Picken (Lisbon, IST). DFTT-60-99, IST-DM-31-99, Nov 1999. 12pp.
e-Print Archive: math.qa/9911015

QUANTUM HOLONOMIES IN (2+1)-DIMENSIONAL GRAVITY.
By J.E. Nelson (Turin U.), R.F. Picken (Lisbon, IST). DFTT-59-99, IST-DM-30-99, Nov 1999. 10pp.
Published in Phys.Lett.B471:367-372,2000
e-Print Archive: gr-qc/9911005

REFLECTIONS ON TOPOLOGICAL QUANTUM FIELD THEORY.
By Roger Picken (Lisbon, IST). DM-IST-9-97, Jul 1997. 8pp.
Talk given at 16th Workshop on Geometric Methods in Physics, Bialowieza, Poland, 20 Jun - 6 Jul 1997.
Published in Rept.Math.Phys.40:295-303,1997
e-Print Archive: q-alg/9707002

CLASSICAL AND QUANTUM GRAVITY. PROCEEDINGS, 1ST IBERIAN MEETING, EVORA, PORTUGAL, SEPTEMBER 21-26, 1992
By M.C. Bento, (ed.) (Lisbon U.), O. Bertolami, (ed.), J.M. Mourao, (ed.), R.F. Picken, (ed.) (Lisbon, IST). 1995.
Singapore, Singapore: World Scientific (1993) 346 p.

NONLOCAL VARIABLES IN QUANTUM GRAVITY AND VASSILIEV INVARIANTS.
By R.F. Picken (Lisbon, IST & Lisbon, IFM). IFM-15-93, Jun 1993. 13pp. Contributed to 2nd Workshop on Constraint Theory and Quantization Methods, Montepulciano, Italy, 28 Jun - 1 Jul 1993.

AN AXIOMATIC DEFINITION OF HOLONOMY.
By A. Caetano (Lisbon U.), R.F. Picken (Lisbon, IST & Lisbon, IFM).
Published in Int. Journ. Math. 5 (1994) 835
IFM-14-93, Sep 1993. 17pp.

LOOP SPACES AND A GEOMETRICAL APPROACH TO PATH INTEGRAL QUANTIZATION.
By R.F. Picken (Lisbon, IST & Lisbon, IFM). IFM-21-92, Jul 1992. 16pp. Contributed to 11th Workshop on Geometric Methods in Physics, Bialowieza, Poland, 7-14 Jul 1992.
In *Bialowieza 1992, Proceedings, Quantization and coherent states methods* 75-89, and Lisbon Nat. Inst. Sci. Invest. - IFM-92-21 (92,rec.Feb.93) 16 p. (304034).

AN INDEX FROM PARASUPERSYMMETRY.
By R.F. Picken (Lisbon, IST & Lisbon, IFM). IFM-18-90, Aug 1990. 16pp.

DYNAMICS OF EUCLIDENIZED EINSTEIN-YANG-MILLS SYSTEMS WITH ARBITRARY GAUGE GROUPS.
By O. Bertolami (Lisbon, IFM), J.M. Mourao (Lisbon, IFM & Lisbon, LIFEP), R.F. Picken (Lisbon, IFM & Lisbon, LIFEP), I.P. Volobuev (Moscow State U.). IFM-9-90, (Received Jul 1990). 50pp.
Published in Int.J.Mod.Phys.A6:4149-4180,1991.

ITO'S STOCHASTIC CALCULUS AND THE BOSONIC STRING.
By R.F. Picken, J.N. Webb (Lisbon, IFM). 1989.
Z. PHYS. C44 (1989) 325-329.

CONSISTENT NONABELIAN ANOMALIES VIA THE FUJIKAWA METHOD.
By F. Freire, R.F. Picken (Lisbon, IFM). IFM-4/89, Mar 1989. 10pp.
Published in Phys.Lett.B222:253,1989.

THE PROPAGATOR FOR QUANTUM MECHANICS ON A GROUP MANIFOLD FROM AN INFINITE DIMENSIONAL ANALOG OF THE DUISTERMAAT-HECKMAN INTEGRATION FORMULA.
By R.F. Picken (Freie U., Berlin & Lisbon, IFM). IFM-13/88, Jun 1988. 25pp.
Published in J.Phys.A22:2285,1989.

DERIVATION OF ANOMALIES USING THE ITO STOCHASTIC CALCULUS.
By R.F. Picken, J.N. Webb (Lisbon, IFM). IFM-14/88, Jun 1988. 11pp.
Published in Int.J.Mod.Phys.A4:3179,1989.

THE DUISTERMAAT-HECKMAN INTEGRATION FORMULA ON FLAG MANIFOLDS.
By R.F. Picken (Freie U., Berlin & Lisbon, IFM). IFM-7/88, Apr 1988. 91pp.
Published in J.Math.Phys.31:616,1990.

GLOBAL ANOMALIES AND HOMOTOPY GROUP COCYCLES.
By R.F. Picken (Freie U., Berlin). 1987.
Lett. Math. Phys. 14 ( 1987) 1-5.

UNIVERSAL CONNECTIONS, GAUGE ANOMALIES AND LIE GROUP COHOMOLOGY.
By R.F. Picken (Freie U., Berlin). Print-86-0180 (FREIE U., BERLIN), Dec 1985. 12pp.
Published in J.Phys.A19:L219,1986.

INTEGRATION ON SUPERMANIFOLDS AND A GENERALIZED CARTAN CALCULUS.
By R.F. Picken, K. Sundermeyer (Freie U., Berlin). Print-85-0325 (BERLIN), Mar 1985. 35pp.
Published in Commun.Math.Phys.102:585,1986.

A QUADRATIC THEORY OF GRAVITY AND ITS COUPLING TO GRAVITINOS.
By R.F. Picken (Freie U., Berlin). Print-84-0144 (BERLIN), Jan 1984. 30pp.

SUPERGROUPS HAVE NO EXTRA TOPOLOGY.
By R.F. Picken (Freie U., Berlin). Print-83-0383 (BERLIN), (Received May 1983). 12pp.
Published in J.Phys.A16:3457,1983.

INSTANTONS WITHOUT TWISTORS.
By R.F. Picken (Freie U., Berlin). FUB/HEP 4/82, (Received Jan 1983). 10pp.

THE RESOLUTION OF THE U(1) PROBLEM.
By R.F. Picken (Queen Mary - Westfield Coll.). Print-82-0422 (QUEEN MARY), (Received Jun 1982). 5pp.
Published in J.Phys.G8:L57,1982.

NEW TOPOLOGICAL INDICES IN SO(3) EINSTEIN YANG-MILLS THEORY.
By R.F. Picken (Queen Mary - Westfield Coll.). Print-80-0885 (QUEEN MARY COLL), (Received Dec 1980). 16pp.
Published in J.Phys.A14:471,1981.

last edited 31/03/2021

roger.picken@tecnico.ulisboa.pt