Friday, April 11
Session Chair: Elena Kosygina, NYU Shanghai
10:00-11:00 Tadahisa Funaki (Beijing Institute of Mathematical Sciences and Applications)
Conservative Dynamic $P(\phi)_2$ Model on the Whole Plane and its Reversible Measures
We consider the conservative dynamic $P(\phi)_2$ model on the whole plane. We show its local well-posedness and the existence of global-in-time solution for a.s.-initial values sampled from a stationary measure. We also construct a family of canonical reversible measures parametrized by harmonic functions and a conserved quantity. This talk is based on joint work with Bin Xie (Shinshu), Qi Zhang (BIMSA) and Hang Zeng (BIMSA).
11:00-11:30 Morning Tea Break
11:30-12:30 Takashi Kumagai (Waseda University)
Quantitative Periodic Homogenization for Symmetric Non-local Stable-like Operators
Recently, homogenization for non-local operators has been studied intensively. So far, these works are mainly devoted to the qualitative results, that is, to determine explicitly the operators in the limit. In this talk, we establish a quantitative homogenization result for symmetric stable-like operators on R^d with periodic coefficients. In particular, we obtain convergence rate for solutions of associated Dirichlet problems on a bounded domain. Our results indicate that the boundary decay behaviors of the solution to the equation in the limit affects the convergence rate in the homogenization. This talk is based on joint works with X. Chen, Z.-Q. Chen and J. Wang.
12:30-14:30 Lunch Break
Session Chair: Vahagn Nersesyan, NYU Shanghai
14:30-15:30 Hao Shen (University of Wisconsin-Madison)
Dynamical Approach to Lattice Gauge Theories
Lattice Yang-Mills or lattice gauge theory are natural lattice models where the field takes values in a matrix group. There are some important questions, such as exponential decay of correlations (mass gap), and uniqueness of infinite volume limit. The Langevin dynamics, or so called stochastic quantization, can be exploited to obtain results in these directions, in a large coupling regime. If time permitted, I will also discuss more general models, such as lattice Yang-Mills coupled with Higgs fields. Based on joint work with Rongchan Zhu and Xiangchan Zhu.
15:30-16:00 Afternoon Tea Break
16:00-17:00 Ryoki Fukushima (University of Tsukuba)
Leading Term of Maximal Edge Traversal Time in First Passage Percolation with Weibull Distribution
In this talk, I will discuss the asymptotic behavior of the maximal edge traversal time in first passage percolation. More precisely, consider the random graph obtained by assigning independent and Weibull distributed positive weights ("traversal time") to the edges of the integer lattice. We are concerned with the shortest path connecting the origin to a remote point. The main result gives sharp asymptotics of the maximal edge traversal time along the shortest path. Based on a joint work with Shuta Nakajima (Meiji University).
