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It is commonly believed that the current problems in the capital markets are a result of the financial models developed by academic mathematicians and industry practitioners. In fact, many of us have been pointingout for years that banks were involved in very risky activities, which produced illusory short term profits. In this talk, I will give a short introduction to the theory behind pricing and hedging derivative contracts (options). A derivative contract is based on an underlying asset. The standard model for the underlying asset price movement assumes that prices evolve according to a random walk with a drift. It is possible for an option seller to set up a hedging portfolio, which is then dynamically rebalanced in response to changes in the underlying asset price. Then, regardless of the random movement of the asset price, the seller of the option is able to pay out the value of the this contract at expiry. There is strong evidence that the normal market behavior assumed by standard models is punctuated by occasional large jumps or drops in prices (e.g. subprime mortgages). These processes are called "jump diffusion" models. A simulation of a trading strategy which exploits these market characteristics shows that bankers can produce apparent profits for many years, followed by enormous losses. The compensation system widely used in the financial sector encourages these sorts of activities. In essence, this bonus system allows executives and traders to be rewarded for apparent short term profits, and to walk away unscathed after producing staggering losses.

More than any thing else technology creates our world. It creates our wealth, our economy, our very way of being," says W. Brian Arthur. Yet, until now major questions related to the evolution of technology have gone unanswered. Where do new technologies come from -- how exactly does invention work? What constitutes innovation, and how is it achieved? Why are certain regions -- Cambridge, England, in the 1920s and Silicon Valley today -- hotbeds of innovation, while others languish? Does technology, like biological life, evolve? How do new industries, and the economy itself, emerge from technologies? In this talk, leading thinkers Lee Smolin, Frances Westley, and Thomas Homer-Dixon discuss economist W. Brian Arthur's work on a boldly original way of thinking about technology that gives answers to these questions.

The stability of spacetime has been related to the production of particles and also to the imaginary parts of the perturbative series. The unitarity relations of the quantum theory impose relations between these two phenomena.