Tuesday, May 26, 2026
10:00 – 10:45 AM Eyal Lubetzky, Courant Institute of Mathematical Sciences, NYU
Shape and Local Laws of the Discrete Gaussian Level Lines
We will discuss two joint works with Joe Chen on the low-temperature (2+1)D integer-valued Discrete Gaussian (ZGFF) model. The level lines were conjectured to have cube-root fluctuations near the sides of the box, mirroring the Solid-On-Solid picture. In the first work, we resolve this and further recover the joint limit law of the top level lines near the sides of the box, which is a product of Ferrari–Spohn diffusions. Building on this, in the second work, we obtain the macroscopic scaling limit of the top level lines, pinpoint the critical window of side-lengths that marks the emergence of each new layer in the surface, and extend the shape and local law results to include the critical window.
10:45 – 11:15 AM Morning Coffee Break
11:15 AM – 12:00 PM Yuri Bakhtin, Courant Institute of Mathematical Sciences, NYU
Differentiability of Shape Functions and Effective Lagrangians
In random environments, the cost/energy of an optimal path between two points grows asymptotically linearly with the distance between those points. The function giving the dependence of the deterministic growth rate on direction is called the shape function. Shape functions are always convex and are conjectured to have no corners or flat edges for a broad class of models. This is related to the KPZ universality. For several classes of models (continuous space polymer models at positive and zero temperatures, HJB equations in dynamic random environments, and anisotropic continuous space FPP models), we show that the shape function is differentiable (i.e., has no corners) and give a formula for its gradient. Joint work with Douglas Dow.
12:00-12:10 PM Group Photo
12:10 – 2:00 PM Lunch Break
2:00 – 2:45 PM Wei Wu, NYU Shanghai
Spin Waves for the XY and Villain Model in d>=3
The XY and the Villain models are models which exhibit the celebrated Kosterlitz-Thouless phase transitions in two dimensions. The spin wave conjecture, originally proposed by Dyson and by Mermin and Wagner, predicts that at low temperature, spin correlations of these models are closely related to Gaussian free fields. I will review the historical background and present some recent progress for the Villain model in d>=3. Based on the joint work with Paul Dario (Cergy). Time permitting, I will also present a massive infrared bound which generalizes the work of Frohlich, Simon and Spencer (based on joint work with Lorenzo Taggi (Sapienza)).
2:45 - 3:00 PM Question time/Short break
3:00 – 3:45 PM Weijun Xu, Westlake University
Interface Motion for 1D Stochastic Allen-Cahn Equation Revisited
Since the original works of Funaki and Brassesco-De Masi-Presutti from 1990's, it has been well known that for the 1D stochastic Allen-Cahn equation starting with a standing wave, the interface location rescale to a diffusion process under proper spacetime scaling. We revisit variants of this problem with some new analytic inputs. These are joint works with Wenhao Zhao (EPFL) and Shuhan Zhou (PKU).
Possible behaviour of the interfaces under a much larger spacetime scaling potentially connect to papers by Fontes-Isopi-Newman-Ravishankar on Brownian web in 2000's.
3:45 – 4:15 PM Afternoon Coffee Break
4:15 – 5:00 PM Siva Athreya, International Centre for Theoretical Sciences
Interplay of Vertex and Edge Dynamics for Dense Random Graphs
The large population limits of opinion dynamics in homogeneous populations, on lattices and on general fixed graphs are quite well understood. We consider a process where the graph itself is dynamic and changes in response to the voter model process, thus creating interaction between the two.
More precisely, we consider a dense random graph in which the vertices can hold opinion 0 or 1 and the edges can be closed or open. The vertices update their opinion at a rate proportional to the number of incident open edges, and do so by adopting the opinion of the vertex at the other end. The edges update their status at a constant rate, and do so by switching between closed and open with a probability that depends on their status and on whether the vertices at their ends are concordant or discordant. We understand the large n limit of this co-evolution and describe the limiting evolution.
This is joint work with Frank den Hollander and Adrian Roellin.