The Narasimhan–Seshadri Theorem establishes a correspondence between stable vector bundles over a compact Riemann surface and unitary representations of the fundamental group of the surface. Since its publication in 1965, this result has played a central role in many branchs of mathematics,including differential geometry, algebraic geometry, low dimensional topology, Teichmueller theory, etc., and more surprisingly in various areas of theoretical physics, like conformal field theory and string theory.

● The goal of this activity is to present a comprehensive view of some of the most important developments that have taken place in the last 50 years derived from the NarasimhanSeshadri Theorem, and explore further directions of the theory.

● The themes to be covered will include: Vector bundles, Principal bundles,Higgs bundles, Parabolic bundles and Higgs bundles, Surface group representations, Gauge theory on higher dimensional Kahler manifolds, Real bundles and Higgs bundles, Geometric Langlands correspondence, Mirror symmetry and Higgs bundles, Irregular connections.

● There will be background talks delivered by the organizing team, historical talks given by Narasimhan and Seshadri, invited research talks, and minicourses.

website: **http://www.cmi.ac.in/~ramadas/NS@50/**

**Syllabus to be covered in terms of modules of 3 (80 minutes) lectures each**

Name of the Speakers with their affiliation, who will cover each module. |
No. of Lectures |
Detailed Syllabus |

1 P. Boalch (Orsay) | 3 | Connections on curves and wild character varieties |

2 O. Biquard (Ecole Polytechnique) | 3 | TBA |

3 S. Gukov (Caltech) | 3 | TBA |

4 T. Pantev (Philadelphia) | 3 | TBA |

5 C. Sabbah (Ecole Polytechnique) | 3 | Twistor Dmodules |

V. Balaji S. Bradlow (Urbana) O. GarciaPrada (Madrid) D.S. Nagaraj N. Nitsure T.R. Ramadas |
1 each | Principal bundles Higher dimension generalizations (Hermitian Einstein connections, etc.) Higgs bundles Parabolic bundles GIT construction of moduli space Moduli of flat connections in physics |

M.S. Narasimhan C.S. Seshadri | 1 each | Historical Overview |