Moduli spaces of singular connections, Character varieties and Geometry of Riemann-Hilbert correspondence.
Event details
| Date | 28.04.2014 |
| Hour | 15:15 › 17:00 |
| Speaker | Masa-Hiko Saito, (Graduate School of Sciences, Kobe University) |
| Location | |
| Category | Conferences - Seminars |
The main topics of this talk are the moduli spaces of connections with
regular or irregular singularities on smooth algebraic curves and the
moduli spaces of generalized monodromy, which are called character
varieties. These two moduli spaces are related to each other by the
Riemann-Hilbert correspondences.
In the first part of this talk, we will discuss about the basic algebraic
constructions of the moduli spaces by GIT due to the work of
Inaba-Iwasaki-Saito and Inaba-Saito.
The moduli spaces of stable parabolic connections with regular or
unramified irregular singularities can be constructed as smooth
quasi-projective symplectic schemes (or manifolds). The moduli spaces of
the monodromy data, links and Stokes data can be constructed as affine
varieties which may have singularities.
We will explain about some beautiful geometry of the Riemann-Hilbert
correspondences which induces isomonodromic foliation on the moduli space
of connections such as Painleve equations.
In the second part of the talk, I will explain about more deep geometric
nature of these moduli spaces such as canonical coordinates induced by the
apparent singularities (a joint work with Szilard Szabo) and two
transversal Lagrangian fibrations in duality (a joint work with C. Simpson
and F. Loray).
regular or irregular singularities on smooth algebraic curves and the
moduli spaces of generalized monodromy, which are called character
varieties. These two moduli spaces are related to each other by the
Riemann-Hilbert correspondences.
In the first part of this talk, we will discuss about the basic algebraic
constructions of the moduli spaces by GIT due to the work of
Inaba-Iwasaki-Saito and Inaba-Saito.
The moduli spaces of stable parabolic connections with regular or
unramified irregular singularities can be constructed as smooth
quasi-projective symplectic schemes (or manifolds). The moduli spaces of
the monodromy data, links and Stokes data can be constructed as affine
varieties which may have singularities.
We will explain about some beautiful geometry of the Riemann-Hilbert
correspondences which induces isomonodromic foliation on the moduli space
of connections such as Painleve equations.
In the second part of the talk, I will explain about more deep geometric
nature of these moduli spaces such as canonical coordinates induced by the
apparent singularities (a joint work with Szilard Szabo) and two
transversal Lagrangian fibrations in duality (a joint work with C. Simpson
and F. Loray).
Practical information
- Informed public
- Free
Organizer
- Tamás Hausel