Germany-Japan

one day workshop on

Geometry and Topology

Waseda University

Nishi-Waseda Campus

Room 51-18-06, 18th floor, Building 51

Monday 22 May 2017

 

This workshop, partially supported by the DAAD-Waseda International Partnership Program, will introduce several related research topics of current interest in geometry and topology.


Campus map (showing Building 51 and Nishi-Waseda Station of the Tokyo Metro Fukutoshin Line)


SPEAKERS:

Peter-Simon Dieterich (University of Hamburg)

TITLE: The ASK/PSK-correspondence and the r-map
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 r-map are mapped to one-parameter deformations of projective special Kähler manifolds in the image of the supergravity r-map. The above one-parameter deformations are interpreted as perturbative alpha'-corrections in heterotic and type-II string compactifications with N=2 supersymmetry. We show that the completeness of the deformed supergravity r-map metric depends solely on the (well-understood) 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 mu-homotopic isolated hypersurface singularities equipped with certain markings. This moduli space can be understood either as a global mu-constant 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 mu-homotopy 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 Cecotti-Vafa on N=2 supersymmetric field theories. Dubrovin showed that it may be interpreted as an isomonodromic deformation, which yields a Riemann-Hilbert correspondence between local solutions of tt*, and monodromy data of an associated meromorphic linear ODE. As a special case, Cecotti-Vafa introduced the tt*-Toda equation, and this was recently investigated by Guest-Its-Lin, and Mochizuki. Motivated by the conjectures of Cecotti-Vafa regarding the symmetrized Stokes matrix S+S^t of the associated linear ODE, and the results of Guest-Its-Lin and Mochizuki, I will describe the moduli space of globally-smooth 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 1-1 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 Seiberg-Witten invariant
ABSTRACT: We construct an invariant of closed spin^c 4-manifolds. This invariant is defined using families of Seiberg–Witten equations and formulated as a cohomology class on a certain abstract simplicial complex. A non-vanishing result of our invariant provides a new class of constraints on configurations of embedded surfaces in a 4-manifold.

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 so-called 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 transpose-dual which is analogous to Arnold's duality. Following this result, it is concluded that transpose-dual pairs extend to a duality of polytopes that are associated to families of K3 surfaces (Ueda-M). In the talk, we discuss that polytope-duality also extends to a duality of Picard lattices of families of K3 surfaces.


SCHEDULE OF TALKS:

Monday 22 May 2017 10:15-17:30

10:15-11:15 Makiko Mase

coffee/tea break

11:30-12:30 Stefan Horocholyn

lunch break

14:00-15:00 Peter-Simon Dieterich

coffee/tea break

15:15-16:15 Falko Gauss

coffee/tea break

16:30-17:30 Hokuto Konno


Organizing committee: Martin Guest (Waseda University), Yasushi Homma (Waseda University)