Welcome address Room: Amphitheater Darboux

Twisted geometries and spin network states

• Simone Speziale (CPT, Marseille)

Room: Amphitheater Darboux Loop quantum gravity is a background-independent approach to the quantization of general relativity. The fundamental states of the theory are described by spin networks, states associated with graphs whose quantum numbers give the spectra of discrete and non-commuting geometric operators. On a fixed graph, the quantum numbers can be interpreted as a collection of fuzzy polyhedra describing a twisted geometry. The maths describing the twisted geometry uses an amusing interplay of symplectic geometry, group theory and Regge geometry which I will describe in some details. There is also a connection to twistors that I will briefly discuss.

Twisted geometries and spin network states

• Simone Speziale (CPT, Marseille)

Room: Amphitheater Darboux Loop quantum gravity is a background-independent approach to the quantization of general relativity. The fundamental states of the theory are described by spin networks, states associated with graphs whose quantum numbers give the spectra of discrete and non-commuting geometric operators. On a fixed graph, the quantum numbers can be interpreted as a collection of fuzzy polyhedra describing a twisted geometry. The maths describing the twisted geometry uses an amusing interplay of symplectic geometry, group theory and Regge geometry which I will describe in some details. There is also a connection to twistors that I will briefly discuss.

Twisted geometries and spin network states

• Simone Speziale (CPT, Marseille)

Room: Amphitheater Darboux Loop quantum gravity is a background-independent approach to the quantization of general relativity. The fundamental states of the theory are described by spin networks, states associated with graphs whose quantum numbers give the spectra of discrete and non-commuting geometric operators. On a fixed graph, the quantum numbers can be interpreted as a collection of fuzzy polyhedra describing a twisted geometry. The maths describing the twisted geometry uses an amusing interplay of symplectic geometry, group theory and Regge geometry which I will describe in some details. There is also a connection to twistors that I will briefly discuss.

Twisted geometries and spin network states

• Simone Speziale (CPT, Marseille)

Room: Amphitheater Darboux Loop quantum gravity is a background-independent approach to the quantization of general relativity. The fundamental states of the theory are described by spin networks, states associated with graphs whose quantum numbers give the spectra of discrete and non-commuting geometric operators. On a fixed graph, the quantum numbers can be interpreted as a collection of fuzzy polyhedra describing a twisted geometry. The maths describing the twisted geometry uses an amusing interplay of symplectic geometry, group theory and Regge geometry which I will describe in some details. There is also a connection to twistors that I will briefly discuss.

Lattice gravity

• Jan Ambjorn (NBI, Denmark)

Room: Amphitheater Darboux Lattice quantum field theory has been very successful as a tool to study non-perturbative aspects of quantum field theory. These lectures describe how the QUANTUM theory of General Relativity can also be formulated as a lattice theory. It is (very) successful in the case of two-dimensional spacetimes. There are several ways to generalize the two-dimensional lattice theory to higher dimensions, but amazingly they lead to the same modified Friedmann equation that seems to resolve all tension present between early time and late time cosmological data. The modified Friedmann equation has no cosmological constant. Instead the present expansion of the universe is caused by the creation of baby universes and links the dynamics of the very early universe to its final destiny.

Lattice gravity

• Jan Ambjorn (NBI, Denmark)

Room: Amphitheater Darboux Lattice quantum field theory has been very successful as a tool to study non-perturbative aspects of quantum field theory. These lectures describe how the QUANTUM theory of General Relativity can also be formulated as a lattice theory. It is (very) successful in the case of two-dimensional spacetimes. There are several ways to generalize the two-dimensional lattice theory to higher dimensions, but amazingly they lead to the same modified Friedmann equation that seems to resolve all tension present between early time and late time cosmological data. The modified Friedmann equation has no cosmological constant. Instead the present expansion of the universe is caused by the creation of baby universes and links the dynamics of the very early universe to its final destiny.

Quantum groups in a (coco) nutshell

• Florian Girelli (U. Waterloo)

Room: Amphitheater Darboux (Lie) Groups are typically seen as encoding a symmetry structure. For some phase spaces, the symmetry structure might need to be equipped with a non-trivial Poisson structure, which must then be compatible with the group product (to have a well defined symmetry action). This defines the notion of Poisson Lie group. When quantizing the system, the Poisson Lie group becomes a quantum group. I will provide a compact introduction to these concepts having in mind as leading example, the 3d (quantum) gravity framework, where such Poisson Lie/quantum symmetries are key to understand the quantum theory.

Quantum groups in a (coco) nutshell

• Florian Girelli (U. Waterloo)

Room: Amphitheater Darboux (Lie) Groups are typically seen as encoding a symmetry structure. For some phase spaces, the symmetry structure might need to be equipped with a non-trivial Poisson structure, which must then be compatible with the group product (to have a well defined symmetry action). This defines the notion of Poisson Lie group. When quantizing the system, the Poisson Lie group becomes a quantum group. I will provide a compact introduction to these concepts having in mind as leading example, the 3d (quantum) gravity framework, where such Poisson Lie/quantum symmetries are key to understand the quantum theory.

Lattice gravity

• Jan Ambjorn (NBI, Denmark)

Room: Amphitheater Darboux Lattice quantum field theory has been very successful as a tool to study non-perturbative aspects of quantum field theory. These lectures describe how the QUANTUM theory of General Relativity can also be formulated as a lattice theory. It is (very) successful in the case of two-dimensional spacetimes. There are several ways to generalize the two-dimensional lattice theory to higher dimensions, but amazingly they lead to the same modified Friedmann equation that seems to resolve all tension present between early time and late time cosmological data. The modified Friedmann equation has no cosmological constant. Instead the present expansion of the universe is caused by the creation of baby universes and links the dynamics of the very early universe to its final destiny.

Lattice gravity

• Jan Ambjorn (NBI, Denmark)

Room: Amphitheater Darboux Lattice quantum field theory has been very successful as a tool to study non-perturbative aspects of quantum field theory. These lectures describe how the QUANTUM theory of General Relativity can also be formulated as a lattice theory. It is (very) successful in the case of two-dimensional spacetimes. There are several ways to generalize the two-dimensional lattice theory to higher dimensions, but amazingly they lead to the same modified Friedmann equation that seems to resolve all tension present between early time and late time cosmological data. The modified Friedmann equation has no cosmological constant. Instead the present expansion of the universe is caused by the creation of baby universes and links the dynamics of the very early universe to its final destiny.

Quantum groups in a (coco) nutshell

• Florian Girelli (U. Waterloo)

Room: Amphitheater Darboux (Lie) Groups are typically seen as encoding a symmetry structure. For some phase spaces, the symmetry structure might need to be equipped with a non-trivial Poisson structure, which must then be compatible with the group product (to have a well defined symmetry action). This defines the notion of Poisson Lie group. When quantizing the system, the Poisson Lie group becomes a quantum group. I will provide a compact introduction to these concepts having in mind as leading example, the 3d (quantum) gravity framework, where such Poisson Lie/quantum symmetries are key to understand the quantum theory.

Quantum groups in a (coco) nutshell

• Florian Girelli (U. Waterloo)

Room: Amphitheater Darboux (Lie) Groups are typically seen as encoding a symmetry structure. For some phase spaces, the symmetry structure might need to be equipped with a non-trivial Poisson structure, which must then be compatible with the group product (to have a well defined symmetry action). This defines the notion of Poisson Lie group. When quantizing the system, the Poisson Lie group becomes a quantum group. I will provide a compact introduction to these concepts having in mind as leading example, the 3d (quantum) gravity framework, where such Poisson Lie/quantum symmetries are key to understand the quantum theory.

Enumeration of bicolored maps: investigating a holographic recursion

• Ariane Carrance

Room: 01

Holography for Higher Spin Gravity

• Robert de Mello Koch

Room: Amphitheater Darboux After a brief review of the original argument due to Maldacena for a holographic duality between IIB string theory on AdS${}_5\times$S${}^5$ and maximally supersymmetric Yang-Mills theory, we turn to the duality between the free O(N) vector model in 2+1 dimensions and higher spin gravity on AdS${}_4$. For this theory we study the spectrum of single trace primaries of the CFT, which is dual to the spectrum of fields in higher spin gravity. By formulating the CFT in terms of bilocal variables, using the formalism of collective field theory, we demonstrate how the gravitational theory can be constructed. This example demonstrates a number of recently discovered phenomena in quantum gravity including the quantum error correction interpretation of holography, entanglement wedge reconstruction and the holography of information.

Holography for Higher Spin Gravity

• Robert de Mello Koch

Room: Amphitheater Darboux After a brief review of the original argument due to Maldacena for a holographic duality between IIB string theory on AdS${}_5\times$S${}^5$ and maximally supersymmetric Yang-Mills theory, we turn to the duality between the free O(N) vector model in 2+1 dimensions and higher spin gravity on AdS${}_4$. For this theory we study the spectrum of single trace primaries of the CFT, which is dual to the spectrum of fields in higher spin gravity. By formulating the CFT in terms of bilocal variables, using the formalism of collective field theory, we demonstrate how the gravitational theory can be constructed. This example demonstrates a number of recently discovered phenomena in quantum gravity including the quantum error correction interpretation of holography, entanglement wedge reconstruction and the holography of information.

Holography for Higher Spin Gravity

• Robert de Mello Koch

Room: Amphitheatre Hermite After a brief review of the original argument due to Maldacena for a holographic duality between IIB string theory on AdS${}_5\times$S${}^5$ and maximally supersymmetric Yang-Mills theory, we turn to the duality between the free O(N) vector model in 2+1 dimensions and higher spin gravity on AdS${}_4$. For this theory we study the spectrum of single trace primaries of the CFT, which is dual to the spectrum of fields in higher spin gravity. By formulating the CFT in terms of bilocal variables, using the formalism of collective field theory, we demonstrate how the gravitational theory can be constructed. This example demonstrates a number of recently discovered phenomena in quantum gravity including the quantum error correction interpretation of holography, entanglement wedge reconstruction and the holography of information.

Holography for Higher Spin Gravity

• Robert de Mello Koch

Room: Amphitheatre Hermite After a brief review of the original argument due to Maldacena for a holographic duality between IIB string theory on AdS${}_5\times$S${}^5$ and maximally supersymmetric Yang-Mills theory, we turn to the duality between the free O(N) vector model in 2+1 dimensions and higher spin gravity on AdS${}_4$. For this theory we study the spectrum of single trace primaries of the CFT, which is dual to the spectrum of fields in higher spin gravity. By formulating the CFT in terms of bilocal variables, using the formalism of collective field theory, we demonstrate how the gravitational theory can be constructed. This example demonstrates a number of recently discovered phenomena in quantum gravity including the quantum error correction interpretation of holography, entanglement wedge reconstruction and the holography of information.

Groups, algebras and hidden symmetries of matrix/tensor models

• Sanjaye Ramgoolam

Room: Amphitheatre Hermite

Groups, algebras and hidden symmetries of matrix/tensor models

• Sanjaye Ramgoolam

Room: Amphitheatre Hermite

Groups, algebras and hidden symmetries of matrix/tensor models

• Sanjaye Ramgoolam

Room: Amphitheatre Hermite

Groups, algebras and hidden symmetries of matrix/tensor models

• Sanjaye Ramgoolam

Room: Amphitheatre Hermite

From random tensors to tensor field theory

• Razvan Gurau (ITP, Heidelberg)

Room: Amphitheatre Hermite Random tensors exhibit a 1/N expansion dominated by melonic graphs. The large N limit of these models is thus richer than the large N limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large N limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the O(N)^3 field theory in the large N limit.

From random tensors to tensor field theory

• Razvan Gurau (ITP, Heidelberg)

Room: Amphitheatre Hermite Random tensors exhibit a 1/N expansion dominated by melonic graphs. The large N limit of these models is thus richer than the large N limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large N limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the O(N)^3 field theory in the large N limit.

From random tensors to tensor field theory

• Razvan Gurau (ITP, Heidelberg)

Room: Amphitheater Darboux Random tensors exhibit a 1/N expansion dominated by melonic graphs. The large N limit of these models is thus richer than the large N limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large N limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the O(N)^3 field theory in the large N limit.

From random tensors to tensor field theory

• Razvan Gurau (ITP, Heidelberg)

Room: Amphitheater Darboux Random tensors exhibit a 1/N expansion dominated by melonic graphs. The large N limit of these models is thus richer than the large N limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large N limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the O(N)^3 field theory in the large N limit.

Peeking at quantum gravity with self-overlapping curves

• Nicolas Delporte (OIST)

Room: 01 After a brief overview of the progress in 2d quantum gravity achieved through JT gravity, we will motivate the study of self-overlapping curves. In particular, we will explore some of their surprising geometrical and combinatorial properties.