ICTP Mathematics Seminar - Monday 26 October at 16:00

[Math Section]

M A T H E M A T I C S  S E M I N A R S  2015

Monday, 26 October, at 16:00 hrs.



Sikander Shehryar (ICTP)


Teichmueller curves and Witten invariants of pseudo-Anosov mapping tori
(Part II)


Abstract:
In his quantum field theoretic interpretation of the Jones polynomial, E.
Witten outlined a construction of a (projective) local system on the
moduli space of curves and used the monodromy representation of this local
system to define 'quantum' invariants of 3-manifolds called mapping tori.
Amongst all mapping tori, pseudo-Anosov mapping tori are the only ones
which are hyperbolic and it is expected that their quantum invariant is
related to their hyperbolic volume. We will show how one can use
Teichmueller curves to compute quantum invariants of pseudo-Anosov mapping
tori.
For concreteness, we will recall the construction of the local system,
which comes from geometric quantization of the moduli space of semi stable
vector bundles or a 2-dimensional conformal field theory, in the case of
genus two curves where it can be explicitly written down. We will compute
the monodromy of this local system restricted to a particular Teichmueller
curve and talk about the pseudo-Anosov mapping tori and their quantum
invariants coming from this example.




VENUE:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first
floor)