# Quantum Crystals and Topological Strings

Domenico Orlando

18.12.2008 at 16:15

Random partitions appear in many branches of mathematics and physics,
such as Gromov-Witten theory, random matrix theory, Seiberg-Witten
theory and others. In particular, the partition function of the
melting crystal corner, given by the MacMahon function, has been shown
to equal the partition function of the topological string A-model with
target space C3. In this talk I will discuss the equivalent crystal
melting problem in two and three dimensions. Particular emphasis will
be given to the quantized version that is deeply related to the XXZ
spin chain. After having shown exact and numerical results I will
discuss the properties of these systems as well their relation to
stochastic quantization, and implications for topological string
theory.
Partly based on 0803.1927[cond-mat.stat-mech].

Arnold Sommerfeld Center

Theresienstrasse 37

Room 348/349