Limit shapes and harmonic tricks

• Nikolai Kuchumov (Abo Academy University)

The talk will be on the tangent plane method — a novel method for analysys of limit shapes of the dimer model. It will consist of three parts. In the first part, we will briefly introduce the dimer model and the necessary concepts, including the associated variational problem. The second part will focus on the use of harmonic and conformal coordinates in the analysis. In the third part, we will consider two specific examples of limit shape: the Aztec diamond with a hole, and a hexagon with a hexagonal hole. If time permits, we will touch a generic parametrization of the limit shape for the lozenge tilings in a simply-connected domain following ideas of R.Kenyon. The talk is based on recent preprint https://arxiv.org/abs/2603.21255.

On the convoy of the ASEP speed process

• Yuan Tian (Universität Leipzig and Max Planck Institute for Mathematics in Sciences)

In this talk, we investigate the size of the convoy in the speed process for the multi-species asymmetric simple exclusion process (ASEP). We present an exact formula for the expected convoy size. We show that the asymptotic expected convoy size is universal for all fixed jump rates $q \in [0,1)$. We further establish a critical scaling \( q = 1 - \gamma/\sqrt{n} \) that yields a nontrivial limiting regime.