The dimer model is one of the simplest but also most intriguing models of statistical mechanics. It is typically studied through its height function, which turns the dimer model into a model of random surfaces. The main question is its large scale behaviour. A remarkable conjecture of Kenyon and Okunkov predicts that the large scale behaviour is in great generality described by the Gaussian free field. This conjecture was proved by Kenyon in the case of Temperleyan boundary conditions. We generalized this result to the piecewise Temperleyan and simply connected domains. Our method is based on considering the spanning tree associated to this model via Temperley’s bijection. As a byproduct, we showed that the a pair of multiple SLE8 reduces to a more standard SLE8(ρ) conditional on the hitting point. This decomposition can also be generated to a more general setting–hypergeometric SLEs. This talk is based on a joint work with Nathana¨el Berestycki and an independent work.

刘明昶，2014年——2018年于清华大学获得理学学士学位；2018年——2023年于清华大学攻读理学博士学位，其中2022年——2023年在奥地利维也纳大学交换。目前已完成博士论文答辩。