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Title: An introduction to twistors Course Description: Twistor theory, introduced by Penrose many years ago, is a way to reformulate massless fields on four-dimensional space-time in terms of an auxiliary 6-dimensional complex manifold, called twistor space. This course will introduce twistor space and the Penrose correspondence (relating fields on twistor space and space-time), at both classical and quantum levels. We will discuss the twistor realization of self-dual Yang-Mills theory and of self-dual gravity. If time permits we will discuss the connection between twistors and celestial holography.

The main focus of this course is the exploration of the symmetry structure of General Relativity which is an essential step before any attempt at a (direct) quantization of GR. We will start by developing powerful tools for the analysis of local symmetries in physical theories (the covariant phase space method) and then apply it to increasingly complex theories: the parametrized particle, Yang--Mills theory, and finally General Relativity. We will discover in which ways these theories have similar symmetry structures and in which ways GR is special. We will conclude by reviewing classical results on the uniqueness of GR given its symmetry structure and discuss why it is so hard to quantize it. In tutorials and homeworks, through the reading of articles and collegial discussions in the classroom---as well as good old exercises---you will explore questions such as "Should general relativity be quantized at all? Is a single graviton detactable (even in principle)?", "What is the meaning of the wave functions of the universe?", "Can we do physics without time?".

This school will be an advanced course on the numerical bootstrap. In the lectures, we will discuss advanced theoretical aspects of numerical bootstrap and algorithms. In the tutorials, we will demonstrate how to use simpleboot/hyperion and help the participants to run bootstrap computation on their own clusters. Main examples are 3D Ising, O(2), O(3), Gross-Neveu-Yukawa CFTs. 

The school will consist of one lecture in the morning and two tutorials in the afternoon (one tutorial for simpleboot (by Ning Su) and another one for hyperion (by Aike Liu).

Course materials, including tutorials, slides, and sample codes, can be found at https://gitlab.com/AikeLiu/Bootstrap-Mini-Course

This event is supported by the Simons Collaboration on The Nonperturbative Bootstrap (https://bootstrapcollaboration.com/). 

https://pirsa.org/C23030

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

Recently we have seen exciting results at the intersection of quantum foundations and the statistical analysis of causal hypotheses by virtue of the centrality of latent variable models to both fields.

In this workshop we will explore how academics from both sides can move the shared frontiers forward. Towards that end, we are including extensive breakout collaboration opportunities in addition to formal presentations. In order to make concrete progress on problems pertinent to both communities, we have selected the topic of causal models with restricted cardinality of the latent variables as a special focus for this workshop. 

Sponsorship for this workshop has been provided by:

https://pirsa.org/C23017

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

Can the effectiveness of a medical treatment be determined without the expense of a randomized controlled trial? Can the impact of a new policy be disentangled from other factors that happen to vary at the same time? Questions such as these are the purview of the field of causal inference, a general-purpose science of cause and effect, applicable in domains ranging from epidemiology to economics. Researchers in this field seek in particular to find techniques for extracting causal conclusions from statistical data. Meanwhile, one of the most significant results in the foundations of quantum theory—Bell’s theorem—can also be understood as an attempt to disentangle correlation and causation. Recently, it has been recognized that Bell’s result is an early foray into the field of causal inference and that the insights derived from almost 60 years of research on his theorem can supplement and improve upon state-of-the-art causal inference techniques. In the other direction, the conceptual framework developed by causal inference researchers provides a fruitful new perspective on what could possibly count as a satisfactory causal explanation of the quantum correlations observed in Bell experiments. Efforts to elaborate upon these connections have led to an exciting flow of techniques and insights across the disciplinary divide. This course will explore what is happening at the intersection of these two fields. zoom link: https://pitp.zoom.us/j/94143784665?pwd=VFJpajVIMEtvYmRabFYzYnNRSVAvZz09

The course is an introduction to quantum field theory in curved spacetime. Upon building up the general formalism, the latter is applied to several topics in the modern theory of gravity and cosmology where the quantum properties of fundamental fields play an essential role.

Topics to be covered:
1) Radiation of particles by moving mirrors 
2) Hawking radiation of black holes  
3) Production of primordial density perturbations and gravity waves during inflation
4) Statistical properties of the primordial spectra  

Required prior knowledge:
Foundations of quantum mechanics and general relativity

This course is designed to introduce machine learning techniques for studying classical and quantum many-body problems encountered in quantum matter, quantum information, and related fields of physics. Lectures will emphasize relationships between statistical physics and machine learning. Tutorials and homework assignments will focus on developing programming skills for machine learning using Python.

We will review the notion of information in the most possible general sense. Then we will revisit our definitions of entropy in quantum physics from an informational point of view and how it relates to information theory and thermodynamics. We will discuss entanglement in quantum mechanics from the point of view of information theory, and how to quantify it and distinguish it from classical correlations. We will derive Bell inequalities and discuss their importance, and how quantum information protocols can use entanglement as a resource. We will introduce other notions of quantum correlations besides entanglement and what distinguishes them from classical correlations. We will also analyze measurement theory in quantum mechanics, the notion of generalized measurements and their importance in the processing and transmission of information. We will introduce the notions of quantum circuits and see some of the most famous algorithms in quantum information processing, as well as in quantum cryptography. We will end with a little introduction to the notions of relativistic quantum information and a discussion about quantum ethics.

This course will introduce some advanced topics in general relativity related to describing gravity in the strong field and dynamical regime. Topics covered include properties of spinning black holes, black hole thermodynamics and energy extraction, how to define horizons in a dynamical setting, formulations of the Einstein equations as constraint and evolution equations, and gravitational waves and how they are sourced.