Purpose of the workshop

The purpose of this workshop is to gather some leading experts in the field and describe the present state of the art. There will be ample time and opportunity for discussions.


Participants

 
Organizer

G. Marinescu


Talks

Ulrich Bunke, Modular Dirac operators and the finvariant
Abstract:
The eta invariant of the Dirac operator on an odddimensional manifold
twisted by a certain bundle of vertex operator algebras is a real
modular form up to integral ones. A partition of the manifold along a
framed hypersurface gives rise to a decomposition of the associated
qexpansion as a sum of the two eta invariants of the components. The
deviation of these eta invariants of manifolds with framed boundary
from integrality and modularity is expressed in terms of the finvariant
of the bordism class of the boundary considered here as a stable
homotopy class of spheres.
Xianzhe Dai, Real analytic torsion form and BismutFreed connection Abstract:
We describe a joint work with Weiping Zhang in which we show
how the real analytic torsion form can come out of the adiabatic
limit of the BismutFreed connection, thus answering a question of
BismutLott.
Sebastian Goette, BismutLott torsion and IgusaKlein torsion Abstract:
As shown by Bismut and Zhang, the Witten deformation can be used to compare analytic torsion invariants with their topological counterparts. We study the Witten deformation of the fibrewise HodgeLaplacian of a family of compact manifolds in the presence of birthdeath singularities. Our results can be used to compare BismutLott and IgusaKlein torsion.
Xiaonan Ma, Superconnection and family Bergman kernels Abstract:
We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection formalism as
in the local family index theorem. This is a joint work with W. Zhang.
Werner Müller, Hyperbolic manifolds, dynamical zeta functions, and analytic torsion Abstract:
We consider the twisted Ruelle zeta function of a
compact hyperbolic manifold of odd dimension. This is a
dynamical zeta function associated to the geodesic flow. A
general conjecture of D. Fried claims that its value at zero
is related to the analytic torsion. We will discuss this
conjecture for a special class of representations of the
fundamental group.
Weiping Zhang, Geometric quantization for proper actions Abstract: We describe a recent joint work with Mathai, in which we establish a
generalization of the GuilleminSternberg geometric quantization conjecture to the
noncompact case of proper action of a noncompact group acting on a noncompact
space with compact quotient. This essentially solves a conjecture of Landsman and
Hochs.
KenIchi Yoshikawa, Analytic torsion and automorphic forms Abstract: Some years ago, we introduced an invariant of K3 surfaces with involution,
which we constructed using equivariant analytic torsion.
This invariant, which is a function on the moduli space, is expressed
as the Petersson norm of an automorphic form. We would like to talk about
the structure of this automorphic form. In many cases, this automorphic form
is expressed as the tensor product of a Borcherds lift and Igusa's modular form.
If time permits, we will talk about the relation between this automorphic form
and the BCOV invariant of some BorceaVoisin threefolds.
The BCOV conjecture suggests that the elliptic modular form appearing
in the Borcherds lift should be equivalent to the elliptic
GromovWitten invariants
of some CalabiYau threefolds.
Guofang Wang, Transverse Kähler geometry of Sasakian manifolds Abstract: By exploiting the transverse Kähler geometry of Sasakian manifolds
we introduced a SasakiRicci flow, which converges (if it does) to an etaEinstein metric (a joint work with K. Smozcyk and Yongbing Zhang).
In the interesting case (the positive case) an
etaEinstein metric can be deformed homothetically to a SasakiEinstein metric. In general there is no convergence and
one can only at most expect to obtain a SasakiRicci soliton. In a joint work with A. Futaki and H. Ono we proved
the existence of SasakiRicci solitons on toric Sasakian manifolds,
one of them is in fact a SasakianEinstein metric.


Program

Thursday, 5.06.08
Seminarraum 2, Mathematisches Institut,
Weyertal 8690.
9:4010:30 U. Bunke 10:5011.40 G. Wang
12:0014:00 Lunch at Haus Brecher
14:0014:50 X. Ma 15:1016:00 X. Dai
Friday, 6.06.08
Seminarraum 3, Mathematisches Institut,
Gyrhofstraße.
10:0010:50 W. Zhang 11:1012:00 S. Goette
12:0014:00 Lunch at Loup de Mer
14:0014:50 K. Yoshikawa 15:1016:00 W. Müller


Supported by


Poster

last modified on
4th of June 2008