Purpose of the workshop
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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.
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Participants
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Organizer
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G. Marinescu
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Talks
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Ulrich Bunke, Modular Dirac operators and the f-invariant
Abstract:
The eta invariant of the Dirac operator on an odd-dimensional 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
q-expansion 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 f-invariant
of the bordism class of the boundary considered here as a stable
homotopy class of spheres.
Xianzhe Dai, Real analytic torsion form and Bismut-Freed 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 Bismut-Freed connection, thus answering a question of
Bismut-Lott.
Sebastian Goette, Bismut-Lott torsion and Igusa-Klein 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 Hodge-Laplacian of a family of compact manifolds in the presence of birth-death singularities. Our results can be used to compare Bismut-Lott and Igusa-Klein 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 Guillemin-Sternberg geometric quantization conjecture to the
noncompact case of proper action of a non-compact group acting on a non-compact
space with compact quotient. This essentially solves a conjecture of Landsman and
Hochs.
Ken-Ichi 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 Borcea-Voisin threefolds.
The BCOV conjecture suggests that the elliptic modular form appearing
in the Borcherds lift should be equivalent to the elliptic
Gromov-Witten invariants
of some Calabi-Yau threefolds.
Guofang Wang, Transverse Kähler geometry of Sasakian manifolds Abstract: By exploiting the transverse Kähler geometry of Sasakian manifolds
we introduced a Sasaki-Ricci flow, which converges (if it does) to an eta-Einstein metric (a joint work with K. Smozcyk and Yongbing Zhang).
In the interesting case (the positive case) an
eta-Einstein metric can be deformed homothetically to a Sasaki-Einstein metric. In general there is no convergence and
one can only at most expect to obtain a Sasaki-Ricci soliton. In a joint work with A. Futaki and H. Ono we proved
the existence of Sasaki-Ricci solitons on toric Sasakian manifolds,
one of them is in fact a Sasakian-Einstein metric.
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Program
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Thursday, 5.06.08
Seminarraum 2, Mathematisches Institut,
Weyertal 86-90.
9:40-10:30 U. Bunke 10:50-11.40 G. Wang
12:00-14:00 Lunch at Haus Brecher
14:00-14:50 X. Ma 15:10-16:00 X. Dai
Friday, 6.06.08
Seminarraum 3, Mathematisches Institut,
Gyrhofstraße.
10:00-10:50 W. Zhang 11:10-12:00 S. Goette
12:00-14:00 Lunch at Loup de Mer
14:00-14:50 K. Yoshikawa 15:10-16:00 W. Müller
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Supported by
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Poster
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last modified on
4th of June 2008