Lecture 1:
Deterministic limit shapes in statistical mechanics
In statistical mechanics states of the system are
distributed randomly according to the Boltzmann law.
However when the size of the system increases,
randomness may manifest itself differently at different
scales. At the macroscopic scale it may develop
deterministic limit shape. Such limit shapes are
usually minimizers of certain functionals which are
determined by the microscopic nature of the system.
The lecture will be focused on the nature of such limit
shapes in dimer models and questions of universality of
fluctuations around various regions of limit shapes.
Lecture 2:
Ice and 6-vertex models in statistical mechanics:
mathematical perspective
The talk will start with a historical overview of
how the model appeared in statistical mechanics.
This will be followed by an overview of some related
combinatorial problems. After this the focus will shift to
the "exact solution" of the model
with periodic boundary conditions followed by the
discussion of algebraic structures involved in the exact
solution (quantum groups with braiding). Then there will
be a brief discussion of other boundary conditions and of
limit shape phenomenon. If time permit, we will see how
the ASEP (Asymmetric Exclusion Process) fits into the
picture.