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A learning seminar on topics related to the geometric aspects of string theory. Several mathematical subjects, such as topology, representation theory, and operator algebras are also discussed. The notes of a few talks are available below.
Time: Thursday 1:00 pm - 3:00 pm Location: Innova 21 Building, Room 5.57 This seminar is organised by Pedram Hekmati and Snigdhayan Mahanta. Kindly contact one of us in order to be included in the mailing-list. Current schedule Semester 2, 2010 ScheduleSpeaker: V. Mathai Title: Twisted K-theory and T-duality Speaker: P. Hekmati Title: Dirac families and fractional loop group I Abstract: In a series of three talks, I will introduce the notion of fractional loop groups LqG and explain how to construct a family of Fredholm operators, parametrised by connections on a circle bundle over LqG, and equivariant with respect to an abelian extension of LqG. The restriction to smooth loops reproduces the usual Dirac family construction in equivariant twisted K-theory of a compact Lie group G. Speaker: P. Hekmati Title: Dirac families and fractional loop group II Speaker: P. Hekmati Title: Dirac families and fractional loop group III Speaker: R. Mickler Title: Ray-Singer torsion and the partition function of a degenerate quadratic functional I Abstract: In the Lagrangian formulation of QFT, the partition functions of certain theories resemble quadratic Gaussian Euclidean integrals over infinite dimensional spaces. After recalling some results about finite dimensional Gaussian integrals, we show that the determinant factors that appear can be generalised to infinite dimensions using techniques of zeta function regularisation. In a paper of Schwarz, it is shown how to apply this regularization scheme to degenerate quadratic functionals, and we investigate the case of Abelian Chern-Simons theory, and explain some of the components of Witten's famous study of CS theory. Speaker: R. Mickler Title: Ray-Singer torsion and the partition function of a degenerate quadratic functional II Abstract: In this talk we continue the discussion of using Schwarz style regularization techniques to study Abelian Chern-Simons theory, a la Witten. We look at what happens in Minkowski signature, when the integrand has a complex prefactor. We show that the regularized version of the signature of a matrix is the famous eta invariant of Atiyah-Patodi-Singer. Speaker: R. Vozzo Title: Introduction to gerbes Abstract: I will give an introduction to the theory of gerbes. I will try to cover bundle gerbes, Hitchin gerbes and PU-bundles. Speaker: S. Mahanta Title: Localisations, completions and derived categories Abstract: The localization of a commutative ring along a multiplicative subset and the completion of such a ring with respect to an ideal will be discussed. Their functorial properties will be explained. Finally the derived category of chain complexes over a unital ring will be described. Speaker: V. Mathai Title: Introduction to parts of the Freed-Hopkins-Teleman program Speaker: S. Mahanta Title: Representable K-theory Abstract: Some basic properties of the representable K-theory of countable inverse limit C*-algebras will be discussed. Speaker: P. Hekmati Title: Construction of loop group central extensions Abstract: I will review basic facts about central extensions of loop groups and provide an explicit geometric construction following Mickelsson and Murray. IGA/AMSI Workshop: "Dirac Operators in Geometry, Topology, Representation Theory, and Physics" Speaker: P. Hekmati Title: Positive energy representations of loop groups Abstract: I will discuss the structure theory of loop groups, and describe the fundamental representation and the Borel-Weil construction of their highest weight representations. Speaker: R. Vozzo Title: String classes and equivariant cohomology Abstract: I will describe a method of defining characteristic classes for principal bundles with structure group the loop group of a compact group. In the case that these are free loops we will see that equivariant cohomology naturally appears. Speaker: S. Mahanta Title: Pro C*-algebras I Abstract: The theory of pro C*-algebras will be discussed following N. C. Phillips. Speaker: S. Mahanta Title: Pro C*-algebras II Abstract: The construction of loop algebras using pro C*-algebras will be explained. Speaker: S. Mahanta Title: On the equivalence of geometric and analytic K-homology I (after Baum-Higson-Schick) Abstract: I shall introduce two mathematical theories, namely, geometric and analytic K-homology. I shall produce a natural transformation from the former to the latter. The main Theorem is that this transformation is actually a natural isomorphism on finite CW complexes. Speaker: S. Mahanta Title: On the equivalence of geometric and analytic K-homology II Abstract: I shall sketch the proof of the equivalence of geometric and analytic K-homology. Last updated: 16 December 2010 |