Réunion d'hiver SMC 2010
Coast Plaza Hotel and Suites, Vancouver, 4 - 6 décembre 2010

Prix de doctorat

Recent generalizations and applications of domino shuffling  [PDF]

Domino shuffling is a random map on the set of domino tilings of the square lattice. It is quite elementary to describe, and has good combinatorial properties; domino shuffling often behaves much like a bijection for enumerative purposes. It was introduced in 1992 by Elkies, Kuperberg, Larsen and Propp for counting domino tilings of Aztec Diamonds.

Since 1992, there have been quite a few generalizations, analyses, and applications of domino shuffling. This work is due to many people, including Borodin, Borodin-Gorin, Dimofte-Gukov, Nordenstam, Petersen-Speyer, Propp, Y., Y.-Cottrell, Y.-Liechty, Y.-Nordenstam, and others (the last two are works in progress). Much of this work has happened in the last two or three years; it spans many areas of mathematics and physics. I will try to give a sense of where the field stands today. I will also describe some of my contributions, including some new constructions of domino shuffles for different lattices, and an application to "box-counting" problems from algebraic geometry.


AARMS: Atlantic Association for Research in the Mathematical Sciences Centre de recherches mathématiques Fields Institute MITACS Pacific Institute for the Mathematical Sciences University of British Columbia Simon Fraser University University of Alberta University of Victoria

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