1 to 2pm: Lunch
2pm:Neil O'Connell (UCD Dublin)
Title: From longest increasing subsequences to Whittaker functions and random polymers
Abstract: The Robinson-Schensted-Knuth (RSK) correspondence is a combinatorial bijection which plays an important role in the theory of Young tableaux and provides a natural framework for the study of longest increasing subsequences in random permutations and related percolation problems. I will give some background on this and then explain how a birational version of the RSK correspondence provides a similar framework for the study of GL(n)-Whittaker functions and random polymers.
3pm: Coffee Break
3.50pm: Kurt Johansson (KTH Stockholm)
Title: The two-time distribution in last-passage percolation
Abstract: I will discuss a new approach to computing the two-time distribution in last-passage percolation with geometric weights. This can be interpreted as the correlations of the height function at a spatial point at two different times in the equivalent interpretation as a discrete polynuclear growth model. I will also discuss the problem of multiple spatial points at the two times. The new approach is closer to standard random matrix theory (or determinantal point process) computations compared to the one in my paper "Two time distribution in Brownian directed percolation", Comm. Math. Phys. 351 (2017).
4.50pm: Sunil Chhita
Title: The two-periodic Aztec diamond
Abstract: Simulations of uniformly random domino tilings of large Aztec diamonds give striking pictures due to the emergence of two macroscopic regions. These regions are often referred to as solid and liquid phases. A limiting curve separates these regions and interesting probabilistic features occur around this curve, which are related to random matrix theory. The two-periodic Aztec diamond features a third phase, often called the gas phase. In this talk, we introduce the model and discuss some of the asymptotic behavior at the liquid-gas boundary. This is based on joint works with Vincent Beffara (Grenoble), Kurt Johansson (Stockholm) and Benjamin Young (Oregon).