## 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.