Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
Path integrals are at the heart of quantum field theory. In spite of their covariance and seeming simplicity, they are hard to define and evaluate. In contrast, functional differentiation, as it is used, for example, in variational problems, is relatively straightforward. This has motivated the development of new techniques that allow one to express functional integration in terms of functional differentiation. In fact, the new techniques allow one to express integrals in general through differentiation.
Similarly to the probability distribution of energy in physics, the probability distribution of money among the agents in a closed economic system is also expected to follow the exponential Boltzmann-Gibbs law, as a consequence of entropy maximization. Analysis of empirical data shows that income distributions in the USA, European Union, and other countries exhibit a well-defined two-class structure. The majority of the population (about 97%) belongs to the lower class characterized by the exponential ("thermal") distribution.
In order to introduce the cosmological constant in a simplicial geometry, constant curvature should be introduced on simplex faces. This yields a compactification of the phase space and the finiteness of the Hilbert for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space.
Quantum effects render black holes unstable. Besides Hawking radiation there is another, genuinely quantum gravitational, source of instability: the Hajicek-Kiefer explosion via tunnelling to a white hole. A recent result in classical general relativity makes this decay channel plausible: there is an exact external solution of the Einstein equations locally (but not globally) isometric to extended Schwarzschild, which describes an object collapsing into a black hole and then exploding out of a white hole. The tunnelling time can in principle be computed using Loop Quantum Gravity.
Niels Bohr was Nobel-winning physicist – a pioneer of quantum theory – but his influence extended far beyond his own research. He was a gifted teacher who established one of the 20th century’s most important centres for physics, and was instrumental in the development of physics worldwide. He became a statesman following the Second World War, calling for international cooperation to avoid nuclear conflict. Bohr’s legacy – in science, humanitarianism, and family – spans generations, as his grandson will illustrate during a special public lecture webcast at Perimeter Institute. Dr.
The theory of resurgence connects perturbative and non-perturbative physics. Focusing on certain one-dimensional quantum mechanical systems with degenerate harmonic minima, I will explain how the resurgent trans-series expansions for the low lying energy eigenvalues follow from the exact quantization condition via the uniform WKB approach. In the opposite spectral region (with high lying eigenvalues), in contrast to the divergent asymptotic expansions expressed as trans-series, the relevant expansions are convergent.
The first lecture will be devoted to the review of the classical theory of the Witten Laplacian, the second -- to the concepts of resurgent analysis. The third -- to applications of the resurgent analysis to the Witten Laplacian. Time permitting, we will touch upon some foundational questions of resurgent analysis.