Leigh Foster, University of Waterloo
Learning Seminar on lozenge tilings and the single dimer model
The study of lozenge tilings and of the dimer model is a well-established area of research, going back to the 1960's and
still subject to active research at present. (Some references, also showing connections to other directions of research,
are listed below.) We will start the learning seminar on this topic with a series of three meetings giving an introduction
to the dimer model in its single-dimer version, and considered on a finite hexagonal grid.
--In the first meeting, on January 27, we will introduce the single dimer model and we will discuss its connection to other
combinatorial objects, with particular emphasis on the connection between the dimer model and the notion of "stack of
boxes".
--In the second meeting, on February 3, we will discuss enumeration questions related to the configurations introduced
in the preceding week.
--The third meeting, on February 10, will be open to requests from the audience. One potential direction for this meeting
will be to look at some probabilistic results on random dimer configurations of a given shape, as well as various limit shape
phenomena, pointing to the study od some intriguing objects called "amoebas".
The learning seminar is intended to continue after the reading week, covering the more recent research topic of double-dimer
and more generally multiple-dimer models.
The seminar is addressed to all interested audiences, with very few assumptions regarding background knowledge.
Come, listen and ask questions - everyone is welcome, and interruptions are hoped for!
MC 5403