PIRSA:09050035 Conference

DOI10.48660/09050035

Conference/School: Connections in Geometry and Physics - 2009

Young, B. (2009). Combinatorics inspired by Donaldson-Thomas theory. Perimeter Institute. https://pirsa.org/09050035

Young, Benjamin. Combinatorics inspired by Donaldson-Thomas theory. Perimeter Institute, May. 09, 2009, https://pirsa.org/09050035 

@misc{ pirsa_PIRSA:09050035,
  doi = {10.48660/09050035},
  url = {https://pirsa.org/09050035},
  author = {Young, Benjamin},
  keywords = {},
  language = {en},
  title = {Combinatorics inspired by Donaldson-Thomas theory},
  publisher = {Perimeter Institute},
  year = {2009},
  month = {may},
  note = {PIRSA:09050035 see, \url{https://pirsa.org}}
}

Abstract

I will describe some combinatorial problems which arise when computing various types of partition functions for the Donaldson-Thomas theory of a space with a torus action. The problems are all variants of the following: give a generating function which enumerates the number of ways to pile n cubical boxes in the corner of a room. Often the resulting generating functions are nice product formulae, as predicted by the recent wall-crossing formulae of Kontsevich-Soibelman. There are now a variety of techniques, both geometric and combinatorial, to compute these formula. My work uses the entirely combinatorial techniques, namely vertex operators and the planar dimer model; these techniques can be applied essentially "bare-handed" and rely very little upon the underlying algebraic geometry.

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