
This workshop, partially supported by the DAADWaseda International Partnership Program, will introduce several related research topics of current interest in geometry and topology.
Campus map (showing Building 51 and NishiWaseda Station of the Tokyo Metro Fukutoshin Line)
SPEAKERS:
PeterSimon Dieterich (University of Hamburg)
TITLE: The ASK/PSKcorrespondence and the rmap
ABSTRACT: We formulate a correspondence between affine and projective special
Kähler manifolds of the same dimension. As an application, we show that,
under this correspondence, the affine special Kähler manifolds in the image
of the rigid rmap are mapped to oneparameter deformations of projective special
Kähler manifolds in the image of the supergravity rmap. The above oneparameter
deformations are interpreted as perturbative alpha'corrections in heterotic
and typeII string compactifications with N=2 supersymmetry. We show that the
completeness of the deformed supergravity rmap metric depends solely on the
(wellunderstood) completeness of the undeformed metric and the sign of the
deformation parameter. This is joint work with V. Cortés and T. Mohaupt.
Falko Gauss (University of Mannheim)
TITLE: The moduli space of marked singularities
ABSTRACT: The moduli space of marked singularities parameterizes muhomotopic
isolated hypersurface singularities equipped with certain markings. This moduli
space can be understood either as a global muconstant stratum or as a Teichmüller
space of singularities. The additional marking allows one to formulate the conjecture
on the analytic behavior of singularities within a distinguished muhomotopy
class in terms of a Torelli type problem in an efficient way. In my talk I will
discuss the history of this problem and introduce carefully the notion of a
marked singularity.
Stefan Horocholyn (Tokyo Metropolitan University)
TITLE: On the Stokes matrices of the tt*Toda equation
ABSTRACT: The tt* equation appeared in the work of CecottiVafa on N=2 supersymmetric
field theories. Dubrovin showed that it may be interpreted as an isomonodromic
deformation, which yields a RiemannHilbert correspondence between local solutions
of tt*, and monodromy data of an associated meromorphic linear ODE. As a special
case, CecottiVafa introduced the tt*Toda equation, and this was recently investigated
by GuestItsLin, and Mochizuki. Motivated by the conjectures of CecottiVafa
regarding the symmetrized Stokes matrix S+S^t of the associated linear ODE,
and the results of GuestItsLin and Mochizuki, I will describe the moduli space
of globallysmooth solutions of tt*Toda in terms of the set of all S such that
S(S^{1})^t has only eigenvalues of unit length. This contains the subset of
all S for which S+S^t > 0, and I will explain why this subset is in 11 correspondence
with an open convex polytope, as well as how it is related to interlacing configurations
of points on the unit circle.
Hokuto Konno (Tokyo University)
TITLE: A cohomological SeibergWitten invariant
ABSTRACT: We construct an invariant of closed spin^c 4manifolds. This invariant
is defined using families of Seiberg–Witten equations and formulated as
a cohomology class on a certain abstract simplicial complex. A nonvanishing
result of our invariant provides a new class of constraints on configurations
of embedded surfaces in a 4manifold.
Makiko Mase (Rikkyo University/Waseda University)
TITLE: Dualities of families of K3 surfaces associated to bimodal singularities
ABSTRACT: It is classically well understood that unimodal singularities have
a socalled Arnold's strange duality that is explained in terms of a duality
among families of K3 surfaces due to Pinkham. It is recently found by Ebeling
and Ploog that some of the pairs of bimodal singularities are transposedual
which is analogous to Arnold's duality. Following this result, it is concluded
that transposedual pairs extend to a duality of polytopes that are associated
to families of K3 surfaces (UedaM). In the talk, we discuss that polytopeduality
also extends to a duality of Picard lattices of families of K3 surfaces.
SCHEDULE OF TALKS:
Monday 22 May 2017 10:1517:30
10:1511:15 Makiko Mase
coffee/tea break
11:3012:30 Stefan Horocholyn
lunch break
14:0015:00 PeterSimon Dieterich
coffee/tea break
15:1516:15 Falko Gauss
coffee/tea break
16:3017:30 Hokuto Konno
Organizing committee: Martin Guest (Waseda University), Yasushi Homma (Waseda University)