prof. Szabo's seminar at SISSA

[Emanuele Tuillier Illingworth]

TIME & VENUE:
Wednesday 23 February 2011, 14:30, lecture room 136 (SISSA Santorio 
Building, I floor)

SPEAKER: Richard J. Szabo

Department of Mathematics
Heriot-Watt University

TITLE: Crystals, instantons and quantum geometry

ABSTRACT:
We describe the statistical mechanics of a melting crystal in three 
dimensions, and its relationships with diverse topics in mathematical 
physics. On the mathematics side, the model is connected to the 
combinatorics of plane partitions and the enumeration of 
Donaldson-Thomas invariants in algebraic geometry. On the physics side, 
it is related to certain integrable hierarchies, matrix models, 
Chern-Simons gauge theory, and a toy model of quantum gravity in six 
dimensions. Its partition function can also be computed by enumerating 
the contributions from noncommutative instantons to a six-dimensional 
topological gauge theory; this yields an interpretation of the melting 
crystal model as a discretization of six-dimensional spacetime at the 
Planck scale. We also describe analogous relations between a melting 
crystal model in two dimensions and N=4 supersymmetric Yang-Mills theory 
in four dimensions.