This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
Quantum computers have the potential to solve certain problems dramatically faster than classical computers. One of the main quantum algorithmic tools is the notion of quantum walk, a quantum mechanical analog of random walk. I will describe quantum algorithms based on this idea, including an optimal algorithm for evaluating Boolean formulas and one of the best known algorithms for simulating quantum dynamics. I will also show how quantum walk can be viewed as a universal model of quantum computation.
Quantum theory is successfully tested in any experimental lab every day. Apart from its experimental validity, quantum theory also constitutes a robust theoretical framework: small variations of its formalism often lead to highly implausible consequences, such as violation of the no-signalling principle or a significant increase of the computational power. In fact, it has been argued that quantum theory may represent an island in theory space. We show that, at the level of correlations, quantum theory may not be as special as initially thought.
The live performance of a drawing contains information, expression and meaning that a finished drawing does not. Part performance, part demonstration, Isabella Stefanescu’s talk will explore the artistic challenges in creating performance pieces with the Euphonopen, an assemblage of hardware and software designed to map the characteristic mark making gestures of an artist to sound.
I will review a recently proposed formalism that describes fluids and superfluids in effective field theory terms. I will then focus on applying this formalism to peculiar string-like objects that exist in fluid systems: vortex lines and vortex rings. These do not obey Newton's second law, and, as a consequence, their behavior is highly counterintuitive. I will describe how effective field theory provides us with an optimal tool to understand how they move and how they interact with one another and with sound.
When we think of a revolution in physics, we usually think of a physical theory that manages to overthrow its predecessor. There is another kind of revolution, however, that typically happens more slowly but that is often the key to achieving the first sort: it is the discovery of a novel perspective on an existing physical theory. The use of least-action principles, symmetry principles, and thermodynamic principles are good historical examples.
One of the central challenges in theoretical physics is to develop non-perturbative methods to describe quantitatively the dynamics of strongly coupled quantum fields. Much progress in this direction has been made for theories with a higher degree of symmetry, such as conformal symmetry or supersymmetry. In recent years the method of localisation has allowed to obtain a great deal of exact results for supersymmetric gauge theories in various dimensions which has led to the discovery of new surprising correspondences such as the celebrated Alday-Gaiotto-Tachikawa correspondence.
In the twentieth century, many problems across all of physics were solved by perturbative methods which reduced them to harmonic oscillators. Black holes are poised to play a similar role for the problems of twenty-first century physics. They are at once the simplest and most complex objects in the physical universe. They are maximally complex in that the number of possible microstates, or entropy, of a black hole is believed to saturate a universal bound.
Mathematics has proven to be "unreasonably effective" in understanding nature. The fundamental laws of physics can be captured in beautiful formulae. In this lecture I want to argue for the reverse effect: Nature is an important source of inspiration for mathematics, even of the purest kind.
Augustine of Hippo declared he knew what time is until someone asked him. After 16 centuries we still largely ignore the true essence of time, but we made definite progress in studying its properties. The most striking, and somewhat intuitively (and tragically) obvious one is the irreversibility of its flow. And yet, our fundamental theories are time-reversal invariant, they do not distinguish between past and future. This is usually accounted for by assuming an immensely special initial condition of the Universe, dressed with statistical arguments.
I will talk about two types of random processes -- the classical Sherrington-Kirkpatrick (SK) model of spin glasses and its diluted version. One of the main motivations in these models is to find a formula for the maximum of the process, or the free energy, in the limit when the size of the system is getting large. The answer depends on understanding the structure of the Gibbs measure in a certain sense, and this structure is expected to be described by the so called Parisi solution in the SK model and Mézard-Parisi solution in the diluted SK model.