Organizer:
Nicolai Reshetikhin
Time and place: Tuesdays 1:00-2:30pm, 891 Evans
Course Control Number: 54608
The seminar will be more in a lecture series formal.
Lectures will be given mostly by Nicolai Reshetikhin.
We will start with the definition of dimer models
on graphs. Then will focus on combinatorics of
dimer configurations on bipartite surface graphs.
Then will discuss the behavior of random dimer configurations
in the limit when the size of the graph grows to infinity.
If time permit we will discuss the conjectures and results
about conformal invariance in the thermodynamical limit.
Calendar:
| September | ||
| 7 | No seminar | |
| 14 | No seminar. | |
| 21 | No seminar. | |
| 28 | Dimer configurations on graphs. The notion of dimer configurations on graphs was introduced. It was should that dimer configurations on surface graphs are equivalent to tiling of the dual cell complex by double tiles. The notion of composition cycles was introduced. The equivalence of rooted spanning trees on a plane graph and dimers on it double graph with two stars removed was explained. Hight functions were introduced. Edge weight systems were introduced and written in terms of height functions. | |
| October | ||
| 5 | Kasteleyn solution for planar dimer models. The plan is to explain the Pfaffian formula for the dimer partition function an to outline the counterpart of this formula for surface graphs. | |
| 12 | Pfaffian formulae for correlation functions. Pfaffian formulae for dimer partition functions and correlation functions on surface graphs of genus "g>0". Bipartite graphs and determinantal formulae for the partition function and for correlation functions. The thermodynamic limit. Periodic graphs. | |
| 19 | After the discussion of special properties of dimer models on the hexagonal lattice, we started to study correlation functions on a hexagonal lattice with toroidal boundary conditions. The integral formula for the correlation kernel was obtained. | |
| 26 | The dimer seminar on this day will be united with the Combinatorics, Geometry , and Representation Theory seminar due to Bown lecture at 4:00pm. The speaker is V. Gorin see here. | |
| November | ||
| 2 | Soibelman's master-class on wall crossing. No seminar. | |
| 9 | Joint seminar with RTG, speaker B. Benedetti. | |
| 16 | Thermodynamical limit for periodic plane graphs. The phase diagram for a planar periodic graph is an ameba of an algebraic curve. Geometrical description of critical waits in terms of isoradial embeddings. | |
| 23 | Critical weights, isoradial embeddings. Variational principle for limit shapes. | |
| 30 | Speaker: P. Di Francesco, (Institut de Physique Theorique,CEA Saclay, France, and MSRI). The proof of the ASM-DPP conjecture. | |
| December | ||
| 7 | No seminar due to the workshop at MSRI. | |