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Representations of the fundamental groups of surfaces appear so often in geometry that it's tempting to see them primarily as geometric structures. In recent years, however, researchers have uncovered beautiful new features of these representations by thinking of them instead as dynamical systems. As an invitation to the dynamical point of view, I'll describe how geometric tools from the study of billiards can be used to build invariants of surface group representations.

Confomal transformations and conformal algebras in D=2 Recap Lecture Six

Twenty-first century finance is built on complex mathematical tools developed by “quants,” a different breed of investor with expertise in fields such as physics, mathematics, and computer science. These models have been the basis for both new trading strategies and new financial products, leading to untold wealth. In some cases, however, these models have done more damage than good, making markets less stable and introducing new systemic risk. In this talk, Dr. James Weatherall will tell the story of how in the aftermath of World War II, some innovative physicists and mathematicians saw surprising connections between physics, gambling, and finance, and put those connections to use to become the first quants. Dr. Weatherall will introduce some of the ideas behind modern quantitative trading and show how the history of mathematical reasoning in finance reveals that these models can be extremely useful-but only if we understand their limitations.