# Research Seminar Series

### Applied Mathematics Seminars

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

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)

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)

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

6 October 2017 13:00 in CM221

(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

6 October 2017 13:00 in CM221

(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

6 October 2017 13:00 in CM221

(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

6 October 2017 13:00 in CM221

(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

6 October 2017 13:00 in CM221

(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

6 October 2017 13:00 in CM221

(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

6 October 2017 13:00 in CM221

(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

6 October 2017 13:00 in CM221

(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

6 October 2017 13:00 in CM221

(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

6 October 2017 13:00 in CM221

(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