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SUMMARY:Moduli spaces of singular connections\, Character varieties and Ge
 ometry of Riemann-Hilbert correspondence.
DTSTART:20140428T151500
DTEND:20140428T170000
DTSTAMP:20260924T071704Z
UID:b09e69e28d6b216e3a9cd0e7f6c138cf652b32eaf70fbe09fc79c43f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Masa-Hiko Saito\, (Graduate School of Sciences\, Kobe Universi
 ty)\nThe main topics of this talk are the moduli spaces of connections wit
 h\nregular or irregular singularities on smooth algebraic curves and the\n
 moduli spaces of generalized monodromy\, which are called character\nvarie
 ties. These two moduli spaces are related  to each other by the\nRiemann-
 Hilbert correspondences.\nIn the first part of this talk\, we will discuss
  about the basic algebraic\nconstructions of the moduli spaces by GIT due 
 to the work of\nInaba-Iwasaki-Saito and Inaba-Saito.\nThe moduli spaces of
  stable parabolic connections with regular or\nunramified irregular singul
 arities can be constructed as smooth\nquasi-projective symplectic schemes 
 (or manifolds).  The moduli spaces of\nthe monodromy data\, links and Sto
 kes data can be constructed as affine\nvarieties which may have singularit
 ies.\nWe will explain about some beautiful geometry of the Riemann-Hilbert
 \ncorrespondences which induces isomonodromic foliation on the moduli spac
 e\nof connections such as Painleve equations.\nIn the second part of the t
 alk\, I will explain about more deep geometric\nnature of these moduli spa
 ces such as canonical coordinates induced by the\napparent singularities (
 a joint work with Szilard Szabo) and two\ntransversal Lagrangian fibration
 s in duality (a joint work with C. Simpson\nand F. Loray).
LOCATION:MAA331 http://plan.epfl.ch/?lang=fr&room=MA+A331
STATUS:CONFIRMED
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