Người trình bàyr: PGS. TS. Wai-Kit Lam, National Taiwan University
Thời gian: 14h Thứ 5, ngày 10/10/2024
Địa điểm: Phòng 507 nhà A6
Link online Zoom: https://us06web.zoom.us/j/81085888082?pwd=n5xXX4oKIE9SLo1x1bTjvOACM52Z7X.1
Meeting ID: 810 8588 8082
Passcode: 123456
Tóm tắt: In first-passage percolation, one puts i.i.d. nonnegative weights on the nearest-neighbor edges of $mathbb{Z}^d$, and studies the induced (pseudo)metric. It is well-known that a metric ball of radius $t$, after rescaled by $1/t$, converges in a certain sense to a deterministic limit shape as $ttoinfty$. However, not too much about the metric ball is known for finite $t$. In this talk, we will discuss the geometry of a ball with a large radius, and we will focus on the boundary of such a ball. We will first talk about the size of the boundary of a ball (based on an earlier joint work with M. Damron and J. Hanson), and then we will talk about holes in a ball (based on a more recent joint work with M. Damron, J. Gold and X. Shen). |
