The mathematical problems arising from modern celestial mechanics, which originated with Isaac Newton’s Principia in 1687, have led to many mathematical theories. Poincaré (1854-1912) discovered that a system of several celestial bodies moving under Newton’s gravitational law shows chaotic dynamics. Earlier, Euler (1707–83) and Lagrange (1736–1813) found instances of stable motion; a spacecraft in the gravitational fields of the sun, earth, and the moon provides an interesting system of this kind. Helmut Hofer, Professor in the School of Mathematics, explains how these observations have led to the development of a geometry based on area rather than distance.
Humanitarianism, which can be defined as the introduction of moral sentiments into human affairs, is a major component of contemporary politics—locally and globally—for the relief of poverty or the management of disasters, in times of peace as well as in times of war. But how different is the world and our understanding of it when we mobilize compassion rather than justice, call for emotions instead of rights, consider inequality in terms of suffering, and violence in terms of trauma? What is gained—and lost—in this translation? In this lecture, Didier Fassin, James D. Wolfensohn Professor in the School of Social Science, attempts to comprehend humanitarian government, to make sense of its expansion, and to assess its ethical and political consequences.
In this survey lecture (which will be continued), I plan to explain basic aspects of the representation theory of finite groups, and how these are applied to various questions regarding expansion and random walks on groups.
The Acculturated Native Who Rebels: Nativists, Nationalists, and Western-Born Jihadists in Historical Perspective
The quest for understanding the origin of our universe has been dramatically transformed since the expansion of the universe was discovered by Edwin Hubble in 1929, thanks to impressive advances in astronomical observations and laboratory experiments. Cosmology is now widely regarded as a precision science. Although confidence in our models has increased, deep questions remain unanswered.
Bodies bound by gravity can evolve in surprising ways. In accord with everyday experience and physical law, heat flows from regions of high to low temperature, and angular momentum from regions of fast to slow spin. However, counter to intuition, in bodies supported by thermal pressure, the hot regions become hotter, whereas in those supported by rotation, the regions of rapid spin spinup. Goldreich will explain this behavior and describe its ultimate consequences.