School of Natural Sciences
A knot is more or less what you think it is—a tangled mess of string in ordinary three-dimensional space. In the twentieth century, mathematicians developed a rich and deep theory of knots. And surprisingly, as Edward Witten, Charles Simonyi Professor in the School of Natural Sciences, explains in this lecture, it turned out that many of the most interesting ideas about knots have their roots in quantum physics.
Prospects in Theoretical Physics is an intensive two-week summer program designed for graduate students and postdoctoral scholars considering a career in theoretical physics. The 2011 program, “Frontiers of Physics in Cosmology,” took place from July 18 to July 29.
In physics, the twentieth century started with the twin revolutions of relativity and quantum mechanics. Much of the second half of the century was devoted to the construction of a theoretical structure unifying these radical ideas, confirmed experimentally to exquisite precision over the past three decades. Yet questions remain. The union of quantum mechanics and gravity strongly suggests that space-time is doomed—but what replaces it?
A knot is simply a tangled loop in ordinary three-dimensional space, such as often causes us frustration in everyday life. Knots are also the subject of a rather rich mathematical theory. In the last three decades, it has unexpectedly turned out that rather deep aspects of the theory of knots are best understood in the context of 20th and 21st century developments in quantum physics.
Quantum theory radically transforms our fundamental understanding of physical reality. It reveals that the world contains a hidden richness of structure that we have barely begun to control and exploit. In this lecture, Frank Wilczek indicates the extraordinary potential ofquantum engineering (the size and nature of Hilbert space); reviews one important ongoing effort to harness it (topological quantum computing); and speculates on its ultimate prospects (quantum minds).
This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools of Mathematics and Natural Sciences.
In this talk, Professor Matias Zaldarriaga discusses the development of the modern study of cosmology, beginning with the discovery of the expansion of the Universe by Edwin Hubble, through current efforts to map the cosmic microwave background, test ideas about the initial conditions of the Universe, and explain the accelerated expansion of the Universe.