Forthcoming Mathematics Seminars at ICTP

[Math]

M A T H E M A T I C S   S E M I N A R S   2008


Tuesday 23 September, at 14:00 hrs

Professor Luca Migliorini
(Università di Bologna, Italy)

"A conjectural description of the weight filtration of the
twisted character variety of a Riemann surface"

Abstract:

The variety parametrizing twisted representations with values in a
reductive group G of the fundamental group of a Riemann surface has a
natural structure of affine smooth variety,   and, as such, has a mixed
Hodge structure, recently investigated by   Hausel and Rodriguez- 
Villegas.
By Hitchin theory, this variety is   diffeomorphic to the moduli  
space of
semistable principal bundles with  a Higgs field.
This moduli space has a natural proper map, the Hitchin fibration,
with target a linear space. We conjecture that the weight filtration of
the cohomology of the character variety coincides with a filtration
naturally associated to the topology of the Hitchin fibration.
We will discuss some evidence for this conjecture and a strategy.
Joint work with M. de Cataldo(SUNY) and T.Hausel(OXFORD)

***

Tuesday 30 September, at 14:00 hrs.

Professor C.S. Aravinda
(TIFR Centre for Applicable Mathematics, Bangalore, India)

"Curvature vs. Curvature Operator"

Abstract : This talk will be of an expository nature, examining the
existence of Riemannian metrics with prescribed signs of sectional
curvature and the curvature operator. We will look at several examples.


VENUE:  SEMINAR ROOM (ICTP Leonardo Building, first floor)