How many times must one shuffle an ordered deck to ensure it is sufficiently randomized? Most recreational players perform only a few shuffles, however, in 1992 Bayer and Diaconis showed, surprisingly, that the magic number is seven. In my talk I will present the 1992 result. I will first introduce a suitable model for the physical process of shuffling cards. Multiple shuffles will then be considered as a probabilistic random walk on S_52. Lastly, through the introduction of a total variation distance, we will show quantitatively that a deck of cards approaches a uniform distribution by seven shuffles.
Understanding Granular Flow through the Intermediate Length Scale
Abstract: While ubiquitous in our everyday lives, granular materials have long resisted a complete theoretical description. In this talk, I will present an overview of our work at MIT to better understand the regime of slow, dense granular flow, a key theme of which has been the use of an intermediate length scale on the order of several grain diameters. In the first half of the talk, I will describe our work using the spot model, where we were able to accurately reproduce flowing dense granular packings, by breaking down the flow into small group displacements of particles. In the second half, I will show that material parameters (such as stress and strain rate) can be successfully interpreted at an intermediate scale, even though they would be intractable at the level of a single particle. It is hoped that these results can aid the formulation of a general continuum theory for granular materials.
The Mathematics of Financial Risk Management
Abstract : Since the remarkable invention of Black-Scholes equation, mathematics has been involved in many financial decisions. Risk management is the practice of controlling the risk of assets and it is one of the realm that mathematics plays an important role. In this talk, we introduce general risk management strategies and explain how they are implemented in the financial industries. No previous knowledge of finance is required.
Origami Geometric Constructions
It is well known what geometric constructions can be carried out in the plane using a straight edge and a compass (and a pencil). Now, if we have a sheet of paper, we can produce a straight line without any instruments, not even a pencil, by folding the sheet. In fact, by making more folds, we can perform less trivial constructions. In this talk we will see that paper folding allows one to do everything that is feasible with a straight edge and a compass, and even some things that are not. As an illustration, we will trisect an (arbitrary) angle and double a cube.
Oh what a tangled web we weave...
...when first we practice to take technology originally used for weaving and, over a century or two, transform it into the computer we know and love today. This talk will give a brief tour of information technology through the ages, with side visits to Jacquard looms, crazy drug-addicted poets, naval empires, and my favorite Hepburn-Tracy movie. If you're lucky, it might also include a guest appearance by the geeky sweater.
Physics and the P vs. NP Problem
In this talk, I'll do a survey of some of the relationships between physics and computational complexity. The talk will progress from the sane (classical and quantum physics) to the imaginative (non-linear corrections to quantum mechanics) to the truly bizarre (anthropic computing, which is when you kill yourself if a computation doesn't go the way you wanted it to). Amazingly, even this last model can be used to generate non-trivial results. No knowledge of complexity theory will be necessary: I'll spend the first 10 minutes or so giving a very brief introduction to the definitions of P, NP, and NP-completeness.
|Coupling, a return from Spring Break presentation
|Hard random walks
|What's the Deal With Entropy and Temperature?!
|Semidefinite Programming and Combinatorial Optimization
|The ubiquity of (formal) languages
|Quantum Fault Tolerance