**16 Oct 2018**

This year’s Mahler Lecturer is Ivan Zachary Corwin, of Columbia University. He will be visiting various Australian universities throughout late October – early November 2018, as outlined below.

### Mahler lecture schedule

- Monday, 29 October: 16:30–17:30; University of Sydney.

Colloquium:*Random permutations, partitions and PDEs*(more …) - Tuesday, 30 October: 11:00–12:00; Univ. Tech. Sydney.

Seminar:*Beyond the Gaussian universality class*(more …) - Wednesday, 31 October: 14:00–15:00; Macquarie University, Sydney.

Public Lecture:*Beyond the Gaussian universality class*(more …) - Thursday, 1 November: 14:00–15:00; Australian National University.

Colloquium:*Beyond the Gaussian universality class*(more …) - Friday, 2 November: 12:00–13:00; LaTrobe University.

Seminar:*Diffusion in random media*(more …) - Monday, 5 November: 15:00–16:00; Monash University.

Colloquium:*Random permutations, partitions and PDEs*(more …) - Tuesday, 6 November: 12:00–13:00; University of Melbourne.

Colloquium:*Diffusion in random media*(more …) - Wednesday, 7 November: 17:00–18:00; University of Melbourne

Public Lecture:*Beyond the Gaussian universality class*(more …) - Thursday, 8 November: 15:00–16:00; University of Adelaide.

Colloquium:*Diffusion in random media*(more …) - Friday, 9 November: 11:00–12:00; University of Queensland.

Colloquium:*Beyond the Gaussian universality class*(more …) - Friday, 9 November: 14:00–15:00; University of Queensland.

Seminar:*Random permutations, partitions and PDEs*(more …)

### Biography

Ivan Corwin is currently a Professor of Mathematics at Columbia University. His thesis included (in joint work with Amir and Quastel) the exact solution to the Kardar–Parisi–Zhang stochastic PDE. Subsequently, with Borodin, he introduced and developed the theory of Macdonald processes. Along with other collaborators, he has developed the area of Integrable Probability, including the study of stochastic vertex models and the Markov duality approach. He has also worked on discrete approximation theory to stochastic PDEs.

Corwin received his Ph.D. from the Courant Institute in 2011 and has since held positions at Microsoft Research, MIT, Institute Henri Poincaré, and now Columbia. He was a Clay Research Fellow and is presently a Packard Fellow, and a Fellow of the Institute of Mathematical Statistics. He was the recipient of the Alexanderson Award, Rollo Davidson Prize, Young Scientist Prize of the IUPAP, and gave an invited lecture at the 2014 ICM.

### Talks & Abstracts

*Beyond the Gaussian universality class*The Gaussian distribution describes fluctuations arising in many systems across mathematics, science and society. However, complex random systems such as those related to interface growth, big data, stochastic optimization, traffic/queuing flow, and stochastic PDEs often do not follow fall into this universality class. This talk will explain how these and other important types of real world systems fall into a different universality class — the so called Kardar–Parisi–Zhang class.The talk is aimed at a very general audience and will feature almost no equations and lots of interesting phenomena, videos and examples.*Random permutations, partitions and PDEs*

We start with a seemingly innocuous question —*what do large random permutations look like?*

Focusing on the structure of their*increasing subsequences*we encounter some remarkable mathematics related to symmetric functions (e.g. Schur and Macdonald), random matrices, and stochastic PDEs.

No prior knowledge of any of this will be assumed.*Diffusion in random media*

In 1827 the botanist Robert Brown observed the seemingly irregular motion of pollen immersed in water. A mathematical model for this*Brownian motion*was proposed later by Einstein in 1905. Since then, it is well validated that motion in quickly mixing random media is well modeled by Brownian motion. In this talk we consider what happens when many particles are released in the same media. Do they behave like independent Brownian motions or does their common environment affect their collective behavior? We will see that the extreme value statistics (i.e., largest displacement) is heavily influenced by the random media and in a one-dimensional model, relying upon some surprising*exact solvability*techniques from quantum integrable systems, we will relate these statistics to random matrix theory and the Kardar–Parisi–Zhang universality class for random growth models.

Absolutely no background is required or expected for this talk.

*The stochastic six vertex model*

From statistical physics to quantum algebra, the six-vertex model has enthralled generations of physicists and mathematicians. In this talk we will discuss a less-studied*stochastic*twist of the model and highlight a few remarkable recent results. Though the talk will touch on topics including the Bethe Ansatz, symmetric function theory and stochastic PDEs, no prior knowledge will be assumed.