Time: 15:00-17:00

Recently there is great progress towards the study of limit random objects in KPZ universality. The full parameter scaling limit of Brownian last passage percolation-the directed landscape, is a kind of random directed metric that is also believed to be the universal limit object of various probabilistic models from integrable to non-integrable cases. The series of lectures aims at showing the construction of such random objects and demonstrate the motivation of such a way of construction from the algebraic aspect. We will further see the interplay between probability, representation theory, and integrable system during the study of directed landscape. After that, we will discuss the stragegy for how to derive the convergence towards the directed landscape.

Besides, we will also talk about how to use directed landscape to connect another universal limit object-KPZ fixed point, a Markov process describing the limit hebavior of a series of random models (TASEP, random polymer, KPZ equation, etc.). We will further show how to use the result from random matrix theory to connect these two objects.

The reference listed below shows some major resources related to the lecture series. The audience needs minimum knowledge from undergraduate probability. Some familarity with random matrix theory and KPZ universality may be helpful.