One Day Probability Event at BiCMR

Talk 1: 10-11 am

Title: Crossing probabilities in 2D critical lattice models

Speaker: Hao WU (Tsinghua University) 

Abstract: This talk has two parts. In the first part, we discuss Ising model which is one of the most studied models in statistical physics. We consider critical Ising model in two-dimensional and give crossing probabilities of multiple interfaces in the critical Ising model in polygon with alternating boundary conditions. Similar formulas also hold for other critical lattice models, for instance level lines of discrete Gaussian free field and Bernoulli percolation. However, the situation is different when one considers uniform spanning tree. In the second part, we discuss uniform spanning tree and explain the corresponding results.

Talk 2: 2-3 pm

Title：An iterative algorithm for Dirichlet problem with random conductance

Speaker: Chenlin GU (NYU Shanghai) 

Abstract: The Dirichlet problem with oscillating coefficients requires a lot of calculation resources in general. We present a new algorithm invented by S. Armstrong, A. Hannukainen, T. Kuusi, J.-C. Mourrat to solve this problem quickly in the context of random conductance. This result makes use of the quantitative homogenization theory and the algorithm can also be generalized to the percolation cluster setting. 

Talk 3: 3:30-4:30

Title: Massless phases for the Villain model in d>=3

Speaker: Wei WU (NYU Shanghai)

Abstract: The XY and the Villain models are mathematical idealization of real world models of liquid crystal, liquid helium, and superconductors. Their phase transition has important applications in condensed matter physics and led to the Nobel Prize in Physics in 2016. However, we are still far from a complete mathematical understanding of the transition. The spin wave conjecture, originally proposed by Dyson and by Mermin and Wagner, predicts that at low temperature, large scale behaviors of these models are closely related to Gaussian free fields. I will review the historical background and discuss some recent progress on this conjecture in d>=3. Based on the joint work with Paul Dario (Tel Aviv).

Contact: 

Ms. He Liu

liuhe@bicmr.pku.edu.cn