ICTP Mathematics Seminar - Wednesday 21 October at 14:30

[Margherita Di Giovannantonio]

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

Wednesday, 21 October, at 14:30 hrs.



Sikander Shehryar (ICTP)


Teichmueller curves and Witten invariants of pseudo-Anosov mapping tori


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)