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.
Seminal work of Steve Lack showed that universal algebraic theories (PROPs) may be composed to produce more sophisticated theories. I’ll apply this method to construct an axiomatic version of the theory of a pair of complementary observables starting from the theory of monoids. How far can we get with this? Quite far! We’ll get a large chunk of finite dimensional quantum theory this way —but the fact that quantum systems have non-trivial dynamics means that it’s (always) possible to present the resulting theory as a composite PROP in Lack’s sense. If time permits,
1. The notion of wall-crossing structure (as defined by Maxim Kontsevich and myself in arXiv: 1303.3253)
provides the universal framework for description of different types of wall-crossing formulas (e.g. Cecotti-Vafa in 2d or KSWCF in 4d). It also gives
a language and tools for proving algebraicity and analyticity of arising generating series (e.g. for BPS invariants).
Inflation is proposed as a means of explaining why the Universe is currently so homogeneous on larger scales, solving both the horizon and flatness problems in early universe cosmology. However, if inflation itself requires homogeneous conditions to get started, then inflation is not a solution to the horizon problem. Most work up until now has focussed on a dynamical systems approach to classifying the stability of inflationary models, but recently Numerical Relativity (NR) has been used to simulate the actual evolution of the inflaton field, leading to new insights.
To build a fully functioning quantum computer, it is necessary to encode quantum information to protect it from noise. Topological codes, such as the color code, naturally protect against local errors and represent our best hope for storing quantum information. Moreover, a quantum computer must also be capable of processing this information. Since the color code has many computationally valuable transversal logical gates, it is a promising candidate for a future quantum computer architecture.
In order to create ansatz wave functions for models that realize topological or symmetry protected topological phases, it is crucial to understand the entanglement properties of the ground state and how they can be incorporated into the structure of the wave function.
Condensed matter realizations of Majorana zero modes constitute potential building blocks of a topological quantum computer and thus have recently been the subject of intense theoretical and experimental investigation. In the first part of this talk, I will introduce a new scheme for preparation, manipulation, and readout of these zero modes in semiconducting wires coated with mesoscopic superconducting islands.
The past few years have seen a surge of interest in six-dimensional superconformal field theories (6D SCFTs). Notably, 6D SCFTs have recently been classified using F-theory, which relates these theories to elliptically-fibered Calabi-Yau manifolds. Classes of 6D SCFTs have remarkable connections to structures in group theory and therefore provide a physical link between two seemingly-unrelated mathematical objects. In this talk, we describe this link and speculate on its implications for future studies of 6D SCFTs.
I will answer the question in the title. I will also describe a new quantum algorithm for Boolean formula evaluation and an improved analysis of an existing quantum algorithm for st-connectivity. Joint work with Stacey Jeffery.
About a decade ago Eynard and Orantin proposed a powerful computation algorithm
known as topological recursion. Starting with a ``spectral curve" and some ``initial data"
(roughly, meromorphic differentials of order one and two) the topological recursion produces by induction
a collection of symmetric meromorphic differentials on the spectral curves parametrized by
pairs of non-negative integers (g,n) (g should be thought of as a genus and n as the number of punctures).
Imagine going beyond treating the symptoms of disease and instead stopping it and reversing it. This is the promise of regenerative medicine.
In her Perimeter Institute public lecture, Prof. Molly Shoichet will tell three compelling stories that are relevant to cancer, blindness and stroke. In each story, the underlying innovation in chemistry, engineering, and biology will be highlighted with the opportunities that lay ahead.