Moduli of vector bundles on compact Riemann surfaces by M.S.Narasimhan
Δημοσιεύτηκε στις 21 Δεκ 2016
20 December 2016, 16:00 to 17:00
VENUE
Ramanujan Lecture Hall, ICTS, Bangalore
The
theory of holomorphic vector bundles on a compact Riemann surface is a
vast "non-abelian" generalisation of the classical theory of the
Jacobian variety. The Jacobian, a complex torus, arose in the work of
Abel, Jacobi and Riemann on abelian integrals on compact Riemann
surfaces. The non-abelian generalisation is achieved by replacing the
homology group by the fundamental group of the surface and considering
unitary representations of the fundamental group.
The theory is
related to Algebraic Geometry, Differential Geometry, Number Theory and
Theoretical Physics. The Speaker will give an overview of some aspects
of the subject.
Some of the topics to be dealt with are :
Algebro-geometric notions of stability of vector bundles and moduli.
Relation to Yang-Mills and conformal field theories.
Geometric Hecke correspondence, which plays a significant role in Geometric Langlands Theory.
VENUE
Ramanujan Lecture Hall, ICTS, Bangalore
The
theory of holomorphic vector bundles on a compact Riemann surface is a
vast "non-abelian" generalisation of the classical theory of the
Jacobian variety. The Jacobian, a complex torus, arose in the work of
Abel, Jacobi and Riemann on abelian integrals on compact Riemann
surfaces. The non-abelian generalisation is achieved by replacing the
homology group by the fundamental group of the surface and considering
unitary representations of the fundamental group.
The theory is
related to Algebraic Geometry, Differential Geometry, Number Theory and
Theoretical Physics. The Speaker will give an overview of some aspects
of the subject.
Some of the topics to be dealt with are :
Algebro-geometric notions of stability of vector bundles and moduli.
Relation to Yang-Mills and conformal field theories.
Geometric Hecke correspondence, which plays a significant role in Geometric Langlands Theory.
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