Friday, September 30, 9:30-5:30 - Morss Hall (Walker Memorial Building, 50-140)
Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community.
| Time | Speaker | Title | Slides |
|---|---|---|---|
| 9:00 - 9:30 | Light Breakfast | ||
| 9:30 - 10:30 | Kenyon | Trees, forests, and limit shapes | Slides [pdf] |
| Abstract:
The uniform spanning tree on Z^2 is just one point of a two-parameter family of measures on "essential spanning forests" in Z^2. These are spanning forests with a positive density of component trees, each with two ends. These measures are also determinantal (for the edge process), but with asymmetric kernel. Using this family we construct scaling limits of spanning forest processes on multiply connected planar domains with fixed boundary connections and paths having prescribed homotopy type. |
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| 10:45 - 11:45 | Sly | First passage percolation on rotationally invariant fields | Slides [pptx] |
| Abstract:
I will discuss new results on continuum models of first passage percolation which are rotationally invariant. For such models we give a multi-scale argument showing that the variance grows as O(n^{1-\epsilon}). Joint work with Riddhipratim Basu and Vladas Sidoravicius |
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| 12:00 - 1:30 | Catered Lunch | ||
| 1:30 - 2:30 | Aizenman | Order - disorder operators in planar and almost planar graphs | Slides [pdf] |
| Abstract: | |||
| 2:45 - 3:45 | Duminil-Copin | Order - disorder operators in planar and almost planar graphs (2) | Slides [pdf] |
| Abstract: In this talk, we provide further details on the proof that boundary spin correlations of almost planar graphs satisfy Pfaffian formulas in the scaling limit. The proof is based on relations between different graphical representations of the Ising model, including the random-current and random-cluster ones. | |||
| 3:45 - 4:30 | Afternoon Break | ||
| 4:30 - 5:30 | Nachmias | Planar maps, random walks and the circle packing theorem | Slides [pdf] |
| Abstract:
Koebe's circle packing theorem ('36) asserts that any planar map can be drawn as a circle packing, that is, the vertex set is drawn in the plane as a set of circles with disjoint interiors such that pairs of circles corresponding to edges of the graph are tangent. We will see how this canonical way of drawing planar maps can be used to study the behaviour of the simple random walk on the map. For instance, a beautiful theorem of He and Schramm ('95) states that when the map is a simply connected infinite triangulation with bounded degrees, the random walk is recurrent (i.e, it returns to the starting vertex with probability 1) if and only if the circle packing of the map has no accumulation points. We will explain how all this relates to electric networks and complex analysis, and discuss some recent extensions (obtained jointly with Angel, Hutchcroft and Ray) to this theory that are used to study random planar maps. |
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