Talks

Logarithmic Sobolev inequalities (LSI) were first introduced by Gross in the 1970s as an equivalent formulation of hypercontractivity. LSI have been well studied in the past few decades and found applications to information theory, optimal transport, and graph theory. Recently matrix-valued LSI have been an active area of research. Matrix-valued LSI of Lindblad operators are closely related to decoherence of open quantum systems.  In this talk, I will present recent results on matrix-valued LSI, in particular a geometric approach to matrix-valued LSI of Lindblad operators. This talk is based on joint work with Li Gao, Marius Junge, and Nicholas LaRacuente.

Understanding IP ownership and ensuring that commercialization of research provides broad societal and economic benefit both in Canada and abroad is extremely important.  Perimeter Institute is also acutely aware that entrepreneurial oriented faculty and graduate students want to engage in commercial enterprise (i.e., through contract research and licensing opportunities with industry or independently with their own research outcomes).  In this colloquium you will learn the basics about the different types of IP protection available and some of the most common pitfalls to avoid.  Hear how IP is used to commercialize technology through licensing or start-up creation. 

Zoom Link: https://pitp.zoom.us/j/99022008403?pwd=NmEzdFJkNlJiRzUvY0VDVERuY3FlUT09

Sampling from classical probability distributions is an important task with applications in a wide range of fields, including computational science, statistical physics, and machine learning. In this seminar, I will present a general strategy of solving sampling problems on a quantum computer. The entire probability distribution is encoded in a quantum state such that a measurement of the state yields an unbiased sample. I will discuss the complexity of preparing such states in the context of several toy models, where a polynomial quantum speedup is achieved. The speedup can be understood in terms of the properties of classical and quantum phase transitions, which establishes a connection between computational complexity and phases of matter. To conclude, I will comment on the prospects of applying this approach to challenging, real-world tasks.

I will present a class of recently computed holographic correlators between half-BPS operators in a vast array of SCFTs with non-maximal superconformal symmetry in dimensions d=3,4,5,6. Via AdS/CFT, these four-point functions are dual to gluon scattering amplitudes in AdS. Exploiting the notion of MRV limit I will show that, at tree level, all such correlators are completely fixed by symmetries and consistency conditions. Our results encode a wealth of novel CFT data and exhibit various emergent structures, including Parisi-Sourlas supersymmetry, hidden conformal symmetry and color-kinematics duality. This talk will be based on https://arxiv.org/pdf/2103.15830.pdf.

A generic low-energy prediction of string theory is the existence of a large collection of axions, commonly known as a string axiverse. String axions can be distributed over many orders of magnitude in mass, and are expected to interact with one another through their joint potential. In this talk, I will show how non-linearities in this potential lead to a new type of resonant energy transfer between axions with nearby masses. This resonance generically transfers energy from axions with larger decay constants to those with smaller decay constants, leading to a multitude of signatures. These include enhanced direct detection prospects for a resonant pair comprising even a small subcomponent of dark matter, and boosted small-scale structure if the pair is the majority of DM. Near-future iterations of experiments such as ADMX and DM Radio will be sensitive to this scenario, as will astrophysical probes of DM substructure.

There exist various scenarios for the very early universe that could potentially be the explanation for the observed properties of the cosmic microwave background. The current paradigm -- inflationary cosmology -- has rightfully received much attention, but it is not the only theoretically viable explanation. Indeed, several alternative scenarios exist, for example a contracting universe prior to a bounce or a slowly expanding emerging universe. It thus bares the question: how can we discriminate between the various theories, both from a theoretical and an observational point of view? A few pathways to answering this question are discussed in this talk.