Katrin Wendland's research
The research results directly related to my Diploma thesis are joint work
with Prof. Werner
They are concerned with
regularized determinants, Ray-Singer analytic torsion, and the Quillen metric,
particularly their dependence on the metric.
Publications building immediately on my PhD project are devoted to
orbifold techniques (partially published
with Sayipjamal Dulat) and with superconformal field theories that can be given
a geometric interpretation on a K3 surface.
In particular, partially in joint work with
Prof. Werner Nahm,
I have investigated the structure of the
moduli space of superconformal field theories on K3,
orbifold conformal field theories on K3, and
mirror symmetry on K3.
These works form the foundation
for my math/physics activities since 2002:
- SCFTs associated to smooth K3 surfaces
- I have found and am investigating explicit constructions of SCFTs associated to smooth K3 surfaces.
- SCFTs associated to Borcea-Voisin threefolds
- Together with Dr. Madeeha Khalid we investigate methods to explicitly construct SCFTs on a certain class of Calabi-Yau threefolds, known as Borcea-Voisin threefolds.
- Limiting processes for CFTs
A project with
Dr. Daniel Roggenkamp
is concerned with limiting processes in CFTs which lead to degeneration
phenomena, yielding geometric structures and thus a conceptual approach to
geometric interpretations to CFTs. We use ideas and techniques from
noncommutative geometry in this project.
- Elliptically fibered Calabi-Yau threefolds and string-string duality
With Dr. Anda Degeratu
we are investigating aspects of the heterotic - type IIA duality from a
mathematical point of view, particularly certain constraints on the geometric
invariants of elliptically fibered Calabi-Yau threefolds arising from this
- On orbifolds and free fermion constructions
With Prof. Ron Donagi
we join the venture to unravel the geometry underlying semi-realistic string
models. Along with a new classification result we have discovered a rather
unexpected connection between certain free fermion constructions and earlier
work by Donagi, Ovrut, Pantev and Waldram which could lead to vast
simplifications of existing techniques. It has already been applied to this
effect by Vaudrevange and his coauthors in the construction of an MSSM with
- Mathieu moonshine
Prof. Anne Taormina
we are investigating the role that finite symplectic symmetry groups of K3
surfaces play in a phenomenon discovered about a decade ago and known as Mathieu moonshine. We
have developed a technique which allows us to combine the symmetry groups of
different Kummer surfaces to larger groups, which vastly exceed the order 960
of the largest finite symplectic automorphism group of any K3 surface, an idea now known as symmetry
surfing. We are first in obtaining representations of such large subgroups of M24
directly from K3 theories, thereby
providing direct evidence for the fact that M24 governs the elliptic
genus of K3. Our joint work with
Prof. Matthias Gaberdiel,
Prof. Anne Taormina
and Dr. Roberto Volpato on symmetries of a special K3 sigma model is related.
- The elliptic genus and its relatives
The as yet conjectural double life of the elliptic genus for a Calabi-Yau
manifold X as regularized U(1)-equivariant index of a Dirac operator on the
loop space of X, on the one hand, and as part of the partition function in
every conformal field theory which describes superstring theory on X, on the
other hand, is at the center of this project. Refinements of the elliptic genus lead to
a number of insights regarding Mathieu Moonshine, as well.
- Topological field theory, integrable systems
This is a project devoted to topological quantum field theories,
which my entire research group was involved in
during its funding through
an ERC Starting Independent Researcher Grant
The Geometry of
Topological Quantum Field Theories. We investigate TERP structures as
described by Hertling, and their role in the study of moduli spaces of
supersymmetric quantum field theories in general and D-branes in particular. In
joint work with Dr. Oliver
Gray, we specifically work on a generalization of Cecotti and Vafa's ADE
classification of superconformal field theories.
The role of integrable systems in the context of ADE type singularities was a main
focus of Dr. Florian Beck's Ph.D. project, supervised by me jointly with PD Dr. Emanuel Scheidegger. As a follow-up to the resulting thesis, in joint work with
Dr. Florian Beck
Prof. Ron Donagi
we have continued to investigate Hitchin and Calabi-Yau integrable systems of BCFG type.
- Mathematical definition of conformal field theory
- In this longterm project, I develop an axiomatic formulation of conformal field theory.