### 10th World Congress in Probability and Statistics

## Plenary Lectures

## Laplace Lecture (Tony Cai)

### Transfer Learning: Optimality and adaptive algorithms

Tony Cai (University of Pennsylvania)

###### Session Chair

Runze Li (Pennsylvania State University)

## Public Lecture (Young-Han Kim)

### Structure and Randomness in Data

Young-Han Kim (University of California at San Diego and Gauss Labs Inc.)

Keywords: Information theory, noise, manufacturing, computer vision, distributed computing, probability laws.

###### Session Chair

Joong-Ho Won (Seoul National University)

## Wald Lecture 2 (Martin Barlow)

### Low dimensional random fractals

Martin Barlow (University of British Columbia)

(1) control of the size of balls (2) control of the resistance across annuli, and (3) a smoothness result (a Harnack inequality). In the ‘low dimensional case’ the Harnack inequality is not needed, and (2) can be replaced by easier bounds on the resistance between points. Many random fractals of interest are low dimensional: examples include critical branching processes, the incipient infinite cluster (IIC) for percolation in high dimensions, and the uniform spanning tree. Critical percolation in d=2 remains a challenge however.

###### Session Chair

Takashi Kumagai (Kyoto University)

## IMS Medallion Lecture (Gerard Ben Arous)

### Random determinants and the elastic manifold

Gerard Ben Arous (New York University)

This is joint work with Paul Bourgade and Benjamin McKenna (Courant Institute, NYU).

###### Session Chair

Arup Bose (Indian Statistical Institute)