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Discrete Markov Wave Maps for Ice Models in Statistical Mechanics

Mathematical Physics and Probability Seminar

Discrete Markov Wave Maps for Ice Models in Statistical Mechanics
Series: Mathematical Physics and Probability Seminar
Location: Online
Presenter: Nick Ercolani, The University of Arizona
Ice Models in statistical mechanics have a rich history of applications in physics going back to Linus Pauling and Elliot Lieb. They also have remarkable connections to combinatorics ranging from studies initiated by Lewis Carroll to more recent explorations by Ian Macdonald.
 
We will focus on the particular example of the Six Vertex Model motivated by trying to view its crystallographic limit in terms of discrete Markov wave maps. Wave maps provide a geometric perspective on wave equations with many conservation laws. We consider, in particular, the box-ball wave maps discussed in recent seminars with Jonathan Ramalheira-Tsu. This can be regarded as paralleling the familiar correspondence between 2D lattice models and the time evolution of 1D quantum spin chains.
 
To amplify this idea we consider the model above the crystal limit from two angles. One uses random matrix theory to study a thermodynamic limit. The other is in terms of quantum groups and their classical limits as a way to understand the Markov character of our wave maps. We will discuss at least one of these and, time permitting, both.