Contents/conteúdo

Mathematics Department Técnico Técnico

LisMath Seminar  RSS

29/04/2016, 16:00 — 17:00 — Room V1.07, Civil Engineering Building, IST
Davide Polini, Universidade de Lisboa

Analytic Continuation Of Chern-Simons Theory

In the study of quantum field theory naturally arises the necessity to deal with infinite-dimensional oscillatory integrals. The purpose of the seminar is to show how the procedure of analytic continuation can make sense of such integrals in some particular cases. We will start with an example of an oscillatory integral in finite dimension given by the Airy function and try to adapt the same strategy to the infinite dimensional case of Chern-Simons action. If time allows it, we will also give an overview of the implications of this idea in physics and knot theory.

Bibliography

  1. E. Witten, Analytic continuation of Chern-Simons theory, Chern-Simons gauge theory 20 (2011): 347-446, arXiv:1001.2933.
  2. H. Murakami, An introduction to the volume conjecture and its generalizations, arXiv:0802.0039.
  3. M. V. Berry and C. J. Howls, Hyperasymptotics, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences,  Vol. 430. No. 1880. The Royal Society, 1990.
  4. M. V. Berry and C. J. Howls, Hyperasymptotics for integrals with saddles, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 434. No. 1892. The Royal Society, 1991.
  5. C. J. Howls, Hyperasymptotics for multidimensional integrals, exact remainder terms and the global connection problem, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences,  Vol. 453. No. 1966. The Royal Society, 1997.

See also

Lismath Seminar.pdf

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