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02/11/2000, 15:45 — 16:45 — Sala P3.10, Pavilhão de Matemática
Carlos Florentino, Instituto Superior Técnico

Coherent state transform and theta functions

02/11/2000, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
Andrei Tyurin, Steklov Mathematical Institute

Three mathematical faces of SU(2)-spin networks

27/07/2000, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
, Macquarie University

A looping of structure

29/06/2000, 17:00 — 18:00 — Sala P3.10, Pavilhão de Matemática
Marco MacKaay, Universidade do Algarve

The holonomy of gerbes with connections II

29/06/2000, 15:15 — 16:15 — Sala P3.10, Pavilhão de Matemática
, Instituto Superior Técnico

Topology of symplectomorphism groups and spaces of symplectic form

29/06/2000, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
, Universidade de Coimbra

Álgebras de Cayley e deformações

25/05/2000, 16:00 — 17:00 — Sala P3.10, Pavilhão de Matemática
Sergei Anisov and Edith Elkind, Instituto Superior Técnico

The joy of quantum computing

25/05/2000, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
Marco Mackaay, Universidade do Algarve

The holonomy of gerbes with connections I

27/04/2000, 15:30 — 16:30 — Sala P3.10, Pavilhão de Matemática
, Faculdade de Ciências, Universidade do Porto

Components of spaces of representations and stable triples

27/04/2000, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
, Instituto Superior Técnico

Symplectic Groupoids and Quantization

30/03/2000, 15:30 — 16:30 — Sala P3.10, Pavilhão de Matemática
, Instituto Superior Técnico

Elliptic cohomology

I will explain how geometric descriptions of genera determine geometric descriptions of the associated cohomology theories and then give some examples. Then I will try to say something about the case of elliptic genera. For these the geometric description is still not rigorous.

References (I have copies of the non-web references, in case any one is interested):

  1. Haven't looked at this paper but it has a cool title: Dijkgraaf, R.; Moore, G.; Verlinde, E.; Verlinde, H., Elliptic genera of symmetric products and second quantized strings. Comm. Math. Phys. 185 (1997), no. 1, 197--209. hep-th/9608096
  2. Witten, Ed., Elliptic genera and quantum field theory. Comm. Math. Phys. 109 (1987), no. 4, 525--536. Postscript from KEK library
  3. Hopkins, Michael J. Characters and elliptic cohomology. Advances in homotopy theory (Cortona, 1988), 87--104, London Math. Soc. Lecture Note Ser., 139, Cambridge Univ. Press, Cambridge-New York, 1989
  4. M. J. Hopkins, M. Ando, and N. P. Strickland, "Elliptic spectra, the Witten genus, and the theorem of the cube", dvi file
  5. Segal, G. "Elliptic cohomology (after Landweber-Stong, Ochanine, Witten, and others)". Séminaire Bourbaki, Vol. 1987/88. Astérisque No. 161-162, (1988), Exp. No. 695, 4, 187--201 (1989).

30/03/2000, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
João Nuno Tavares, Faculdade de Ciências, Universidade do Porto

Sobre o método do referencial móvel de E. Cartan

Bibliografia:

A. Na exposição seguirei muito de perto:

  1. Cartan Elie, La theorie des groupes finis et continus et la geometrie differentielle. Gauthiers-Villars, 1937.
  2. Cartan Elie, La methode du repere mobile, la theorie des groupes continus et les espaces generalises. Hermann, 1935.

B. Outras referências mais actuais e avançadas (que eu não vou abordar):

  1. Griffiths P., On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry. Duke Math. Journal 41 (1974), 775-814.
  2. Griffiths P., Harris J., Algebraic geometry and local differential geometry. Ann. Sci. Ecole Norm. Sup. 12 (1979), 355-452.
  3. Akivis M. A., Goldberg V. V., Projective differential geometry of submanifolds. North-Holland, 1993.
  4. Akivis M. A., Goldberg V. V., Conformal differential geometry and its generalizations. John Wiley and Sons, Inc., 1996.

C. Aplicações (que eu não vou abordar):

  1. Razumov A. V., Frenet Frames and Toda Systems, math.DG/9901023
  2. Fels, M., Olver, P. J., Moving coframes I. A practical algorithm. Acta Appl. Math. 51 (1998) 161-213.
  3. Fels, M., Olver, P. J., Moving coframes II. Regularization and theoretical foundations. Acta Appl. Math. 55 (1999) 127-208.

17/02/2000, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
, Instituto Superior Técnico

The topology of the moduli space of vector bundles and the Verlinde formula

17/02/2000, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
Gonçalo Rodrigues, Instituto Superior Técnico

Spin Foams and models of gravity

16/12/1999, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Louis Crane, Kansas State University, USA

The representation theory of the Quantum Lorentz Algebra andapplications to quantum gravity

16/12/1999, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
Nuno Romão, Cambridge University

Constraints on monopole spectral curves

25/11/1999, 16:30 — 17:30 — Sala P3.10, Pavilhão de Matemática
, Universidade do Algarve

TQFT's: A new approach

25/11/1999, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
, Instituto Superior Técnico

Quantum holonomies in $(2+1)$-dimensional gravity and quantum matrix pairs

In this talk we describe some recent results relating, on the one hand, to a method of quantizing a model of gravity in two space and one time dimensions, and on the other, to an algebraic structure - quantum matrix pairs - appearing in this context, which has many similarities with quantum groups.

References:

  1. J. E. Nelson and R. F. Picken, Quantum holonomies in (2+1)-dimensional gravity, gr-qc/9911005.
  2. J. E. Nelson and R. F. Picken, Quantum matrix pairs, math.QA/9911015.

25/11/1999, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
, Grupo de Física Matemática, Universidade de Lisboa

Geometry, stochastic calculus and quantum fields in a non-commutative space-time

21/10/1999, 16:30 — 17:30 — Sala P3.10, Pavilhão de Matemática
, Instituto Superior Técnico

Chern-Simons gauge theory and Vassiliev invariants

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Organizadores correntes: Roger Picken, Marko Stošić.

Projecto FCT PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry.

CAMGSD FCT