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Department of Mathematical Sciences

Research Seminar Series

Applied Mathematics Seminars

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Arithmetic Study Group

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Centre for Particle Theory Colloquia

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Computing Seminars/Talks

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


CPT Student Seminar

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Departmental Research Colloquium

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Distinguished Lectures and Public Lectures

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Geometry and Topology Seminar

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Informal HEP Journal club

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Maths HEP Lunchtime Seminars

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Pure Maths Colloquium

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Statistics Seminars

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


Stats4Grads

Maths HEP Lunchtime Seminars: Minisuperspace Quantum Supersymmetric Cosmology (and its Hidden Kac-Moody Structures)

Presented by Philippe Spindel, U.Mons

6 October 2017 13:00 in CM221

I describe the quantisation of the dimensional reduction to one timelike dimension of N=1, D=4 supergravity on a SU(2) group manifold, taking into account all nonlinear fermionic terms of the dynamic. The quantisation leads to a 64 dimensional Hilbert space that provides a representation of operators from which the supersymmetric and Hamiltonian constraints are built. These operators generate a representation of the maximally compact sub-algebra $K(AE_3)$ of the rank-3 Kac-Moody algebra $AE_3$. The quartic-in-fermions term of the Hamiltonian constraint presents remarkable algebraic and physical properties, one of them being a possible quantum avoidance of the cosmological singularity. Moreover a 50 dimensional subspace of the Hilbert space admit propagating solutions of the constraint equations that carry a chaotic spinorial dynamic described asymptotically by reflection operators generalising the classical Coxeter relations and defining a spinorial extension of the Weyl group of $AE_3$.

(based on arXiv : 1406.1309, Phys. Rev. D 90 (2014) 10, 103509; arXiv : 1704.08116, Phys. Rev. D 95 (2017) 12, 126011)

Contact daniele.dorigoni@durham.ac.uk or jyotirmoy.bhattacharya@durham.ac.uk for more information


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