THE (one and only) RANDOM GRAPH

Persi Diaconis, Stanford University

Abstract: 

Imagine n people connected by random links (for each pair of people, connect them or not with probability 1/2). This makes a connection graph. If you make another (with the same people, but new connections) the chance that the two graphs are 'the same' is tiny (of course). Now think about n= infinity. Strange but true: the chance that two such graphs are 'the same' is certain. this object 'THE random graph and it has amazing properties. It's so strange, it's almost weird enough to get you doubting that there really is an infinity (is there?). I've been using such things (with the logician Maryanthe Milliarias) to show that certain things that we would like to 'get our hands on' are impossible to describe. Years of thinking make it seem so and this is one way of proving things. I will explain all this 'In English' for a general audience.

Other links:

• Dr. Diaconis' homepage. 

• Dr. Diaconis talking about card shuffling or fair dice on Numberphile!

The Art of Maths

Chris Budd, University of Bath

Abstract: 

Mathematics and art are more similar than is commonly thought. Each is concerned with the process of being highly creative with abstract objects and of producing everlasting work of great aesthetic beauty. 

In this talk I will look at early art inspired by geometry, symmetry, numbers and algebra. I will then look at the role mathematics has played in the art of the Renaissance. Next I will consider mathematics’ influence on other artistic forms, taking us up to the work of Escher and how this inspired the study of Fractals. I will  conclude with a bit of mathematical dancing.

Other links:

• Dr. Budd's homepage. 

• A fun and inspiring talk by Dr. Budd on creative and playful math.

The Art of Deception - Encountering Perception as a Creative Material

Shiry Ginosar, University of California, Berkeley

Abstract:

Computer Vision has made great strides forward in the last decade, and yet, the perception of vision systems is still impoverished. Current systems excel at tasks that are easy to define and evaluate, such as the classification of images and the detection of objects. However, they fail to capture the things that really matter to humans, such as the non-verbal, detailed information that is essential for the majority of everyday human behaviors. In my work, I am trying to push the limits of computer vision toward such a rich perception. I will cover several projects that take steps in this direction by mining for temporal changes in historical data, using multimodal data to learn about interpersonal communication, and modeling individual appearances. Through these examples, I will discuss some of the tools needed to learn rich representations directly from big data. In particular, I will focus on the human visual system and how we can utilize its capabilities and limitations for producing realistic-looking synthetic content.

Other links:

• Dr. Ginosar's homepage. 

• Dr. Ginosar on Great Big Story, talking about yearbook photos!

Patterns in Number Theory - Misleading or True?

Peter Sarnak, Princeton University

Abstract: 

The theory of numbers offers a fertile ground for finding patterns and conjectures. Large data samples can be misleading and in many cases what is true remains speculative. We will discuss a few examples in the theory of prime numbers and diophantine equations.

Other links:

• Dr. Sarnak's homepage.

• Learn about Dr. Sarnak's mathematical journey in this CIRM interview!