PIRSA:16050048 Scientific Series Mathematical physics

DOI10.48660/16050048

Series: Mathematical Physics

Williams, H. (2016). Cluster Theory is the Moduli Theory of A-branes in 4-manifolds. Perimeter Institute. https://pirsa.org/16050048

Williams, Harold. Cluster Theory is the Moduli Theory of A-branes in 4-manifolds. Perimeter Institute, May. 19, 2016, https://pirsa.org/16050048 

@misc{ pirsa_PIRSA:16050048,
  doi = {10.48660/16050048},
  url = {https://pirsa.org/16050048},
  author = {Williams, Harold},
  keywords = {Mathematical physics},
  language = {en},
  title = {Cluster Theory is the Moduli Theory of A-branes in 4-manifolds},
  publisher = {Perimeter Institute},
  year = {2016},
  month = {may},
  note = {PIRSA:16050048 see, \url{https://pirsa.org}}
}

Abstract

We'll explain the slogan of the title: a cluster variety is a space associated to a quiver, and which is built out of algebraic tori.

They appear in a variety of contexts in geometry, representation theory, and physics. We reinterpret the definition as: from a quiver (and some additional choices) one builds an exact symplectic 4-manifold from which the cluster variety is recovered as a component in its moduli space of Lagrangian branes. In particular, structures from cluster algebra govern the classification of exact Lagrangian surfaces in Weinstein 4-manifolds.

This is joint work with Vivek Shende and David Treumann.

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