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Topological Quantum Field Theory Seminar   RSS

Past sessions

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27/04/2000, 14:00 — 15:00 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Symplectic Groupoids and Quantization

30/03/2000, 15:30 — 16:30 — Room P3.10, Mathematics Building
, 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 — Room P3.10, Mathematics Building
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 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

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

17/02/2000, 14:00 — 15:00 — Room P3.10, Mathematics Building
Gonçalo Rodrigues, Instituto Superior Técnico

Spin Foams and models of gravity

16/12/1999, 15:00 — 16:00 — Room P3.10, Mathematics Building
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 — Room P3.10, Mathematics Building
Nuno Romão, Cambridge University

Constraints on monopole spectral curves

25/11/1999, 16:30 — 17:30 — Room P3.10, Mathematics Building
, Universidade do Algarve

TQFT's: A new approach

25/11/1999, 15:00 — 16:00 — Room P3.10, Mathematics Building
, 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 — Room P3.10, Mathematics Building
, 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 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Chern-Simons gauge theory and Vassiliev invariants

21/10/1999, 15:00 — 16:00 — Room P3.10, Mathematics Building
Paulo Almeida, Instituto Superior Técnico

Noncommutative geometry: a flash

21/10/1999, 14:00 — 15:00 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Geometric quantization of the space of flat connections on a Riemann surface

19/02/1998, 16:50 — 17:50 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Vacuum of N=2 supersymmetric Yang-Mills theory

Introduction to the solution by Seiberg and Witten of the N=2 supersymmetric Yang-Mills theory (following the reference).

Reference

  • W. Lerche, "Introduction to Seiberg-Witten Theory and its Stringy Origin", hep-th/9611190 .

19/02/1998, 15:20 — 16:20 — Room P3.10, Mathematics Building
Margarida Mendes Lopes, Faculdade de Ciencias, Universidade de Lisboa

Blow-up of points in almost general position and Del Pezzo surfaces

Geometric description of singularities in Del Pezzo surfaces.

Reference:

  • J.-Y. Merindol, "Les Singularites Simples Elliptiques, Leurs Deformations, les Surfaces Del Pezzo et les Transformations Quadratiques", Ann. Scient. Ec. Norm. Sup., 4 serie, 15 (1982) 17-44

19/02/1998, 14:15 — 15:15 — Room P3.10, Mathematics Building
, Faculdade de Ciências, Universidade do Porto

Introduction to deformation quantization - III

Preparatory material for deformation quantization distributed during the meetings by Joao Nuno.

22/01/1998, 16:50 — 17:50 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Introduction to F-theory II

Continuation of the study of aspects of the relation between

  1. moduli spaces of flat E 8 connections on elliptic curves,
  2. the deformation of complex structures on Del Pezzo surfaces and,
  3. singularities on these surfaces,

are studied. The motivation comes from work on "F-theory" by Friedman, Morgan and Witten.

References

  • R. Friedman, J. Morgan and E. Witten, "Vector Bundles and F theory" hep-th/9701162
  • R. Friedman, J. Morgan and E. Witten, "Vector Bundles over Elliptic Fibrations", alg-geom/9709029.
  • R. Friedman, J. Morgan and E. Witten, "Principal G-bundles over elliptic curves", alg-geom/9707004 .

22/01/1998, 15:20 — 16:20 — Room P3.10, Mathematics Building
, Instituto Superior Tecnico

Geometric methods in integrable systems

Study equations in Lax form and understand how they give rise to a spectral curve and a line bundle on it.

References:

  • Mumford, D. "Tata Lectures on Theta, vol II", Progress in Math. 43, Birkhauser 1984
  • Beauville, A. "Jacobiennes des courbes spectrales et systemes hamiltoniens completement integrables", Acta Math. 164, '90

22/01/1998, 14:15 — 15:15 — Room P3.10, Mathematics Building
, Faculdade de Ciências, Universidade do Porto

Introduction to deformation quantization

Preparatory material for deformation quantization distributed during the meetings by Joao Nuno.

Current organizers: Roger Picken, Marko Stošić.

FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.

 

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