First Passage Percolation and Related Models

“首通道渗流及相关模型”研讨会将于2020年7月27日至8月14日在印度班加罗尔的国际理论科学中心举行。本次研讨会将重点介绍随机生长的概率模型——首通道渗流（first-passage percolation， FPP）及其相关模型的最新研究进展。这是当代概率论中一个活跃的研究领域，与统计物理学有着重要的联系。讲习班的一部分将专门用于培训这些主题的研究生和早期职业研究人员。该奖项将为研讨会的美国参与者提供旅行支持。在二维上，FPP是一个猜想上属于KPZ普适类的模型，它由几个描述表面生长过程的模型组成。KPZ类模型与随机矩阵理论、渐近表示理论和数论密切相关。物理学家将FPP和相关模型作为随机介质中的聚合物模型或磁性界面模型进行研究，生物学家将其作为细菌生长的伊甸园模型进行研究。在一类用可积概率的方法在某种意义上“完全可解”的这类亲属上，已经取得了很大的进展。然而，即使在启发式的物理层面上，这些模型在可解决的特殊情况之外也很难理解；例如，对于大于2的维度，几乎没有任何结果。与其他关于fpp型模型的会议不同，ict研讨会将强调可积或精确可解框架之外的方法。通过专注于超越精确可解性的技术，研讨会将把参与者团结起来，解决更广泛的科学界感兴趣的基本问题。该研讨会的网站保存在https://www.icts.res.in/program/FPP2020.This。奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The workshop First-Passage Percolation and Related Models will take place at the International Center for Theoretical Sciences in Bangalore, India, July 27-Aug 14, 2020. This workshop will be devoted to presenting the latest research progress on the first-passage percolation (FPP), a probabilistic model of random growth, and closely related models. This is currently an active research area in contemporary probability theory and has important connections to statistical physics. Part of the workshop will be devoted to training graduate students and early career researchers in those topics. This award will provide travel support for the US based participants in the workshop.In two dimensions, FPP is a model that is conjecturally in the KPZ universality class, which consists of several models describing surface growth processes. Models in the KPZ class are intimately related with random matrix theory, asymptotic representation theory and number theory. FPP and related models have also been studied by physicists as a model for polymers in a random medium or as model of magnetic interfaces, and by biologists as the Eden model of bacterial growth. Much progress has been made on a class of these relatives which are in some senses "exactly solvable" by the methods of integrable probability. However, even at the physics level of heuristic, these models are poorly understood outside of solvable special cases; for instance, there are hardly any results for dimensions larger than 2. Unlike other conferences on FPP-type models, the ICTS workshop will emphasize methods outside of the integrable or exactly solvable framework. By focusing on techniques beyond exact solvability, the workshop will unify participants around solving fundamental problems of interest to the broader scientific community. The workshop website is maintained at https://www.icts.res.in/program/FPP2020.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.