Columbia Mathematics Department Colloquium
Groupoids and the Riemann-Hilbert correspondence
by
Marco Gualtieri
University of Toronto
Abstract:
The relationship between a flat connection and its
monodromy is known as the Riemann-Hilbert correspondence.
It forms the foundation of our understanding of ordinary differential
equations, and is ubiquitous in the theory of integrable systems.
We will describe a precise analogy with the correspondence between
the representations of a Lie algebra and those of its associated
simply-conencted Lie group. This leads us to construct a new family
of Lie groupoids / stacks which underlie the Riemann-Hilbert correspondence.
monodromy is known as the Riemann-Hilbert correspondence.
It forms the foundation of our understanding of ordinary differential
equations, and is ubiquitous in the theory of integrable systems.
We will describe a precise analogy with the correspondence between
the representations of a Lie algebra and those of its associated
simply-conencted Lie group. This leads us to construct a new family
of Lie groupoids / stacks which underlie the Riemann-Hilbert correspondence.