Recent research activity

Prof. Francesco Toppan

(Associate Professor II, CCT/CBPF, MCT)

Research area:

Algebraic methods applied to dynamical systems.

Integrable systems.

Supergravity, String Theory and M-theory.

Braid groups: representations and cryptography.

Leader of the research group (CNPq approved):

Algebraic structures in Field Theory.

Awards and grants:

- Polish Academy of Science 2003 Prize.

- CNPq productivity grant PQ, 2003-2006.

Supervisions (concluded):

1) M. Rojas, Master, CBPF, May 2000.

2) H. L. Carrion Salazar, Ph.D., CBPF, July 2003.

Supervising student:

M. Rojas, Ph.D. (CAPES/CBPF)

IC program students:

1) Sergio Canova - undergraduate (IME)

2) Guilherme Veríssimo - undergraduate (IME)

Recent courses:

- String Theory, second semester 2000 (Oct.-Dec.) .

- Chiral Algebras and Applications to Physics, first semester 2001 (Apr.-Jun.)

- String Theory, second semester 2001 (Oct.-Dec.).

- Spinors, Clifford Algebras and Generalized Supersymmetries,

first semester 2002 (Apr.-Jun.).

- Spinors, Clifford Algebras and Generalized Supersymmetries,

first semester 2003 (Apr.-Jun.).

Referee activity for journals:

Birkhauser Verlag. Journal of Nonlinear Mathematical Physics, Physica A.

Referee activity for international scientific projects:

National Commission of Scientific and Technologic Investigation,

CONICYT/FONDECYT, Chile, 2003-2004.

Collaborator of Concise Encyclopedia of Supersymmetry (Kluwer)

Homepage: www-home.univer.kharkov.ua.duplij/susy/susy2000.html

Referee activity for external (international) Ph.D. thesis:

Gil Emil Schieber, Ph.D. (University of Provence, Aix-Marseille I), September 2003.

Classification de systemes conformes 2D et groupes quantiques.

Participation in Ph.D. & Master thesis commissions::

- Daniel G. Gomes Sasaki, Ph.D. (CBPF), February 2000.

Um Teorema de Não Renormalização para o Linking Number em Três Dimensões.

- Moises Porfírio Rojas Leyva, Master (CBPF), May 2000.

Rediscutindo a Trialidade de Cartan.

- Guillermo S. Cuba Carrillo, Ph.D. (CBPF), September 2000.

Aspectos algébricos e geométricos dos modelos de Toda.

- João F. de Medeiros Neto, Ph.D. (CBPF), January 2001.

Aspectos de Bosonização Funcional em (2+1)D.

- Raphael D. Martins De Paola, Ph.D. (CBPF), January 2001.

Aspectos de Teoria Quântica de Campos: o Vácuo e algumas Aplicações.

- Fabio A. da Costa Carvalho Chalub, Ph.D. (IMPA), May 2001.

Huigens’ Principle for Dirac Operators.

- Marcelo S. Sarandy, Ph.D. (CBPF), December 2001.

Finitude em Teoria Quântica de Campos: um Estudo Algébrico.

- Lúcio Souza Fassarella, Ph.D. (CBPF), May 2002.

Simetrias Modulares e Localização Modular em Física Quântica Local.

- Yoni Walter Milla Gonzales, Master (CBPF), October 2002.

Átomos excitados/cavidades.

- Sortelano Araújo Diniz, Ph.D. (CBPF), April 2003.

Yang-Mills Supersimétrico. Multipleto de Matéria com Massa Induzida.

- Hector Leny Carrion Salazar, Ph.D. (CBPF), July (2003).

Os octonions e suas aplicacoes na fisica.

(President of the commission).

International Collaborations:

Prof. Ashok Das, University of Rochester, USA.

On Integrable Systems.

Theoretical Physics Laboratory at JINR, Dubna, Russia:

Prof. Evgeny Ivanov, Prof. Sergey Krivonos, Prof. Anatol Pashnev.

On Supersymmetric Field Theories.

Prof. Jerzy Lukierski, University of Wroclaw, Poland.

On Extended Supergravity, M-theory.

Prof. Ziemowit Popowicz, University of Wroclaw, Poland.

On Supersymmetric Intagrable Systems.

Prof. Jorge Zanelli, CECS, Valdivia, Chile.

On Chern-Simons Supergravities.

Visited institutions in the last two years:

University of Stockholm, Sweden.

Joint Institute for Nuclear Research (JINR, Dubna, Russia).

Universidade de Padova, Italy.

University of Wroclaw, Poland.

CECS, Valdivia, Chile.

Recent seminar activity:

UFRJ, September 2000

IMPA, December 2000

CBPF, September 2000,

CBPF, November 2000

University of Stockholm, Sweden, February 2001.

4 research seminars at CBPF, Oct.-Nov. 2001.

Seminars on Extended Supersymmetries, jointly with the

Ph.D. students H.L. Carrion e M. Rojas, Nov. 2001.

University of Padova, Italy, January 2002.

University of Wroclaw, Poland, February and August 2002.

University of Wroclaw, Poland, February and August 2003.

CBPF, April 2003.

CECS, Valdivia, Chile, cycle of two seminars, June 2003.

University of Santiago, Chile, June 2003.

Invited lecturer in international conferences:

- Workshop on Super and Quantum Field Theory, Dubna, July 2000.

- 2nd Volkov´s Memorial Conference, Kharkov, July 2000.

- Conference on Group Theoretical Methods in Physics, Dubna, August 2000.

- NATO ARW Workshop on Supersymmetry and Quantum Groups, Kiev,

September2000.

- XXXVII Karpacz Winter School in Theoretical Physics, February 2001.

- IX Conference on Supersymmetry, SUSY 2001, Dubna, Russia, June 2001.

- Workshop on Quantum Gravity in Superstrings, Dubna, Russia, June 2001.

- Workshop “The Quantum Structure of Spacetime”, Corfu, September 2001.

- Workshop Born-Ogievetsky em Karpacz, September 2001.

- Workshop on “Integrable Field Theories, Solitons and Duality”, IFT/UNESP, S.

Paulo, Brazil, July 2002.

- International Conference: Ideas of A.A. Michelson in Math. Physics (Bedlewo,

Poland), August 2002.

- II International Londrina Winter School in Mathematical

Physics (CCE - Un. Est. de Londrina), Brazil, August 2002.

- SILAFAE IV, Aguas de Lindóia, Brazil, October 2002.

- International Conference: Renormalization Group and Anomalies in Gravitation

and Cosmology, Ouro Preto, UFJF (MG), Brazil, March 2003.

- Workshop on Supersymmetry and Quantum symmetries SQS´03, JINR, Dubna,

Russia, July 2003.

Summer/Winter School Lectures:

- On Classical Anomalies no Quantum Gravity in Superstrings, Programa Heisenberg

Landau Bogoliubov Infeld Program, Dubna, Russia, June 2001.

- Algebraic Structures and Classification Methods in the Search for a Theory Of

Everything, IV Escola do CBPF, July 2002 .

- On the Octonionic M-theory, II Summer School in Modern

Mathematical Physics, Institute of Physics, Belgrad and Max-Planck Institute,

Muenchen. Kopaonik (Yugoslavia), September 2002.

Participation in Brazilian events:

- XXII Encontro Nacional de Física de Campos e Partículas, São Lourenço, October

2001. Oral presentation: Anomalies in Classical Dynamical Systems. Two

panels jointly with the Ph.D. students H.L. Carrion e M. Rojas.

- XXIII Encontro Nacional de Física de Partículas e Campos, Águas de Lindóia, SP,

October 2002.

- XXIV Encontro Nacional de Física de Partículas e Campos, Caxambu, MG,

October 2003. Oral presentation: Exceptional Structures in Mathematics and Physics.

One panel jointly with the Ph.D. students H.L. Carrion and M. Rojas.

Works published in peer reviewed international journals since

September 2001:

1) F. Toppan, Division Algebras, Extended Supersymmetries and Applications,

Nucl. Phys. B (Proc. Suppl.) 102 & 103 (Sep. 2001) 270-277.

2) M.A. De Andrade, M. Rojas and F. Toppan, The Signature Triality of Majorana-

Weyl Spacetimes, Int. J. Mod. Phys. A., vol. 16 n. 27 (Oct. 2001) 4453-4479.

3) A. Pashnev and F. Toppan, On the Classification of N-extended Supersymmetric

Quantum Mechanical Systems, J. of Math. Phys., vol. 42, n.11 (Nov. 2001)

5257-5271.

4) F. Toppan, on Anomalies in Classical Dynamical Systems, J. of Nonlin. Math.

Phys., vol.8, n. 3 (Nov. 2001) 518-533.

5) H.L. Carrion, M. Rojas and F. Toppan, An N=8 Superaffine Malcev Algebra and

Its N=8 Sugawara, Phys.Lett. A, vol. 291, n. 2-3 (Dec. 2001) 95-102.

6) A.Constandache, A. Das and F. Toppan, Lucas Polynomials and a Standard Lax

representation for the polytropic gas dynamics, Lett. Math. Phys. vol. 60 (June

2002) 197-209.

7) J. Lukierski and F. Toppan, Generalized Space-time Supersymmetries,

Division Álgebras and Octonionic M-theory, Phys. Lett. B vol. 539 (Jul. 2002)

266-276.

8) F. Toppan, On the Octonionic M-superalgebra, Journal of High Energy Physics,

vol. PRHEP unesp2002/39 (Dec. 2002) 1-17.

9) H.L. Carrion, M. Rojas and F. Toppan, Residual Symmetries in the Presence of an

EM Background, Mod. Phys. Lett. A vol. 18 (March 2003) 629-641.

10) H.L. Carrion, M. Rojas and F. Toppan, Division Algebras and the N=2,4,8

Superextended KdVs, Journal of Physics A, vol. 36 (March 2003) 3809-3820.

11) H.L. Carrion, M. Rojas and F. Toppan, Octonionic Realizations of One-

dimensional Extended Supersymmetries. A Classification, Mod. Phys. Lett. A,

18 (March 2003) 787-798.

12) H.L. Carrion, M. Rojas and F. Toppan, Quaternionic and Octonionic Spinors.

A Classification, Journal of High Energy Physics JHEP 04 (April 2003) 40

1-28.

13) F. Toppan, On the Octonionic Superconformal M-algebra,

Int. J. Mod. Phys. A 18 (May 2003) 2135-2141.

14) J. Lukierski and F. Toppan, Octonionic M-Theory and D=11 Generalized

Conformal and Superconformal Algebras, Phys. Lett. B 567 (August 2003),

125-132.

15) Z. Popowicz e F. Toppan, The N=2 Supersymmetric Heavenly Equation and its

Super-Hydrodynamical Reductions, Journal of Physics A 36 (September 2003),

9701-9709.

Published proceedings for international conferences:

1) F. Toppan, Triality of Majorana-Weyl Spacetimes with Different Signatures,

Proceedings of the JINR Workshop "Supersymmetries and Quantum

Symmetries SQS'99", JINR, Dubna (2000) 440-445.

2) F. Toppan, Classifying N-Extended 1-Dimensional Supersymmetric Systems,

NATO ARW Meeting, Kiev, Sept. 2000.

Non Commutative Structures in Mathematics and Physics (S. Duplij e J.

Wess eds.), Kluwer Ac. Press, Holanda, (2001) 195-201.

3) F. Toppan, Division Algebras and Extended SuperKdVs, XXXVII Karpacz Winter

School in Theoretical Physics.

New Developments in Fundamental Interaction Theories,

AIP Conf. Proc. 589 (2001) 439-445.

4) F. Toppan, Affine Malcev Algebra and N=8 KdV, IX Conference on Supersymmetry

and Unification of Fundamental Interactions, SUSY2001.

Supersymmetry and Unification of Fundamental Interactions,

World Scientific (2002) 424-426.

5) F. Toppan, Centrally Extended Residual Symmetries in the Presence of a Constant

EM Background, Supersymmetries and Quantum Symmetries SQS’01,

Proceedings do XVI Max Born Symposium, Karpacz 2001. Published in

Dubna, JINR (2002) 194-201.

6) F. Toppan, On the Octonionic M-algebra and Superconformal M-algebra. Preprint

CBPF-NF-016/03. Lecture Notes II Summer School in Modern

Mathematical Physics, Kopaonik (YU).

Proceedings published in Brazilian journals:

1) F. Toppan, Anomalous Effects in Classical Dynamical Systems.

Proceedings XXII Encontro Nacional de física

de Partículas e Campos, S.Lourenço, October 2001. SBF,

www.sbf1.if.usp.br/eventos/enfpc/xxii, 16 pages.

2) F. Toppan, Generalized Space-time Supersymmetries and Octonionic M-theory.

Proceedings do XXIII Encontro Nacional de física

de Partículas e Campos, Águas de Lindoia, October 2002. SBF,

www.sbf1.if.usp.br/eventos/enfpc/xxiii, 4 pages.

3) F. Toppan, Estruturas algébricas na busca da teoria do todo. Álgebras de Clifford,

espinores e supersimetria. Lecture Notes IV Escola do CBPF.

CBPF publication 2003.

Monographies:

1) F. Toppan, Lecture Notes: String Theory and Zeta-function, Preprint

CBPF-MO-002/00, November 2000. (String Theory course).

2) F. Toppan, Division Algebras and Physics, Preprint CBPF-MO-002/01,

November 2002 (Lecture Notes).

3) F. Toppan, Elementary Topology, Preprint CBPF-MO-004/02, May 2002,

(Lecture Notes for IV Escola do CBPF).

Rio de Janeiro, 10/06/03.