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.


Current Research Interests

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



Teaching

Undergraduate teaching
Master's and PhD courses (none this current semester)


Publications and preprints

Invariants and TQFT's for cut cellular surfaces from finite 2-groups
By Diogo Bragança, Roger Picken. submitted to Bol. Soc. Port. Mat.
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 25/01/2017

rpicken@math.ist.utl.pt