Professor Elizabeth Winstanley
School of Mathematical and Physical Sciences
Professor
e.winstanley@sheffield.ac.uk
+44 114 222 3796
+44 114 222 3796
G5, Hicks Building
Full contact details
Professor Elizabeth Winstanley
School of Mathematical and Physical Sciences
G5
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
School of Mathematical and Physical Sciences
G5
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Profile
-
I was born in Wigan, Lancashire and educated at Abbey Gate College, Saighton Grange, near Chester. I did my MA (1992) and DPhil (1996) at St. Hugh's College, Oxford University. From 1996-2000 I was the Fellow and Tutor in Applied Mathematics at Oriel College, Oxford, before I moved to a lectureship at the University of Sheffield in September 2000.
- Research interests
-
My research interests lie in general relativity, black holes and quantum field theory in curved space-time. Current projects include:
- Rotating quantum states
- Asymptotically Anti-de Sitter black holes
- QFT of charged scalar fields
- QFT on anti-de Sitter space-time
- Publications
-
Show: Featured publications All publications
Featured publications
Journal articles
- Hadamard renormalization for a charged scalar field. Classical and Quantum Gravity. View this article in WRRO
- Vacuum polarization on topological black holes. Classical and Quantum Gravity, 35(23). View this article in WRRO
- Analysis of scalar and fermion quantum field theory on anti-de Sitter
space-time. International Journal of Modern Physics D. View this article in WRRO
- Black holes with SU(N) gauge field hair and superconducting horizons. Journal of High Energy Physics, 2017(1). View this article in WRRO
All publications
Books
- Quantum Black Holes. Springer Berlin Heidelberg.
- Preface.
- Introduction. Springer Berlin Heidelberg.
Journal articles
- Charge superradiance on charged BTZ black holes. The European Physical Journal C, 84(6), 594.
- Renormalized stress-energy tensor on global anti-de Sitter space-time with Robin boundary conditions. General Relativity and Gravitation, 56(4). View this article in WRRO
- Superradiance and quantum states on black hole space-times. Journal of Physics: Conference Series, 2531(012011).
- Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions. General Relativity and Gravitation, 55.
- Quantization of a charged scalar field on a charged black hole background. Physical Review D, 106(12).
- Vortical effects for free fermions on anti-de Sitter space-time. Symmetry, 13(11).
- Vacuum polarization on topological black holes with Robin boundary conditions. Physical Review D, 103(4).
- Quantum field theory on global anti-de Sitter space-time with Robin boundary conditions. Classical and Quantum Gravity, 38(3). View this article in WRRO
- Quantum superradiance on static black hole space-times. Physics Letters B, 811.
- Hadamard parametrix of the Feynman Green’s function of a five-dimensional charged scalar field. International Journal of Modern Physics D. View this article in WRRO
- Hadamard renormalization for a charged scalar field. Classical and Quantum Gravity. View this article in WRRO
- Vacuum polarization on topological black holes. Classical and Quantum Gravity, 35(23). View this article in WRRO
- Analysis of scalar and fermion quantum field theory on anti-de Sitter
space-time. International Journal of Modern Physics D. View this article in WRRO
- Thermal expectation values of fermions on anti-de Sitter space-time. Classical and Quantum Gravity, 34(14). View this article in WRRO
- Black holes with SU(N) gauge field hair and superconducting horizons. Journal of High Energy Physics, 2017(1). View this article in WRRO
- Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity. Physics Letters B, 764, 87-93. View this article in WRRO
- Solitons and hairy black holes in Einstein-non-Abelian-Proca theory in anti-de Sitter spacetime. Physical Review D - Particles, Fields, Gravitation and Cosmology, 94(4). View this article in WRRO
- Stability of gravitating charged-scalar solitons in a cavity. Physical Review D - Particles, Fields, Gravitation and Cosmology, 94(2). View this article in WRRO
- Vacuum for a massless quantum scalar field outside a collapsing shell in anti-de Sitter space–time. General Relativity and Gravitation, 48(8). View this article in WRRO
- Instability of sphaleron black holes in asymptotically anti-de Sitter space-time. Physics Letters B, 758, 239-243. View this article in WRRO
- Rotating fermions inside a cylindrical boundary. Physical Review D, 93(10). View this article in WRRO
- On the stability of dyons and dyonic black holes in Einstein–Yang–Mills theory. Classical and Quantum Gravity, 33(4), 045003-045003. View this article in WRRO
- Topological black holes insu(N)Einstein–Yang–Mills theory with a negative cosmological constant. Physics Letters B, 753, 268-273. View this article in WRRO
- On the stability of soliton and hairy black hole solutions of . Journal of Mathematical Physics, 57(2), 022506-022506. View this article in WRRO
- Renormalised fermion vacuum expectation values on anti-de Sitter space–time. Physics Letters B, 749, 597-602. View this article in WRRO
- The global rotating scalar field vacuum on anti-de Sitter space–time. Physics Letters B, 740, 188-191. View this article in WRRO
- Hawking emission from quantum gravity black holes. JHEP, 1111, 075-075. View this article in WRRO
- Higher-dimensional solitons and black holes with a nonminimally coupled scalar field. Physical Review D, 80(10). View this article in WRRO
- Angular profile of emission of non-zero spin fields from a higher-dimensional black hole. PHYS LETT B, 680(4), 365-370. View this article in WRRO
- On the existence of soliton and hairy black hole solutions of su(N) Einstein-Yang-Mills theory with a negative cosmological constant. CLASSICAL QUANT GRAV, 25(24). View this article in WRRO
- Information erasure and the generalized second law of black hole thermodynamics. INT J THEOR PHYS, 47(6), 1692-1698. View this article in WRRO
- Neutrino telescope modelling of Lorentz invariance violation in oscillations of atmospheric neutrinos. ASTROPART PHYS, 29(5), 345-354. View this article in WRRO
- Abundant stable gauge field hair for black holes in anti-de Sitter space.. Phys Rev Lett, 100(1), 011301. View this article in WRRO
- Bulk emission of scalars by a rotating black hole. J HIGH ENERGY PHYS(6). View this article in WRRO
- Vacuum polarization for lukewarm black holes. PHYS REV D, 77(2). View this article in WRRO
- Soliton and black hole solutions of su(N) Einstein-Yang-Mills theory in anti-de Sitter space. Physical Review D, 76(10). View this article in WRRO
- Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes. General Relativity and Gravitation, 39(10), 1719-1734. View this article in WRRO
- Brane decay of a ( 4+n)-dimensional rotating black hole. III: spin-1/2 particles. J HIGH ENERGY PHYS(3). View this article in WRRO
- Probing quantum decoherence in atmospheric neutrino oscillations with a neutrino telescope. Astroparticle Physics, 25(5), 311-327. View this article in WRRO
- Brane decay of a (4+n)-dimensional rotating black hole II: spin-1 particles. Journal of High Energy Physics, 2006(2). View this article in WRRO
- Brane decay of a (4+n)-dimensional rotating black hole: spin-0 particles. Journal of High Energy Physics, 2005(9). View this article in WRRO
- Lorentz and CPT invariance violation in high-energy neutrinos. Physical Review D, 72(6). View this article in WRRO
- Conformally coupled scalar solitons and black holes with negative cosmological constant. Physical Review D, 72(2). View this article in WRRO
- Thermodynamics of de Sitter black holes with a conformally coupled scalar field. Physical Review D, 72(2). View this article in WRRO
- Dressing a black hole with non-minimally coupled scalar field hair. Classical and Quantum Gravity, 22(11), 2233-2247. View this article in WRRO
- Probing quantum decoherence with high-energy neutrinos. Physics Letters B, 609(3-4), 206-211. View this article in WRRO
- Static axially symmetric solutions of Einstein-Yang-Mills equations with a negative cosmological constant: Black hole solutions. Physical Review D, 70(8). View this article in WRRO
- Instability of a four-dimensional de Sitter black hole with a conformally coupled scalar field. Physical Review D, 70(6). View this article in WRRO
- On the existence of conformally coupled scalar field hair for black holes in (anti-)de Sitter space. Foundations of Physics, 33(1), 111-143. View this article in WRRO
- On the linear stability of solitons and hairy black holes with a negative cosmological constant: the even-parity sector. Classical and Quantum Gravity, 19(4), 689-723. View this article in WRRO
- Classical super-radiance in Kerr-Newman-anti-de Sitter black holes. Physical Review D, 64(10). View this article in WRRO
- On the linear stability of solitons and hairy black holes with a negative cosmological constant: the odd-parity sector. Classical and Quantum Gravity, 18(11), 2125-2146. View this article in WRRO
- Renormalized black hole entropy in anti-de Sitter space via the "brick wall" method. Physical Review D, 63(8). View this article in WRRO
- D-particle recoil space-times and "glueball" masses. International Journal of Modern Physics A, 16(2), 251-265. View this article in WRRO
- Renormalized stress tensor in Kerr space-time: General results. Physical Review D, 62(8).
- Monopole black hole skyrmions. CLASSICAL QUANT GRAV, 17(20), 4161-4174. View this article in WRRO
- Infinitely coloured black holes. CLASSICAL QUANT GRAV, 17(7), 1595-1611. View this article in WRRO
- Renormalized stress tensor in Kerr space-time: General results. PHYS REV D, 62(8). View this article in WRRO
- Do stringy corrections stabilize colored black holes?. PHYS REV D, 61. View this article in WRRO
- Logarithmic operators fold D branes into AdS(3). PHYS LETT B, 476, 165-171. View this article in WRRO
- Divergence of a quantum thermal state on Kerr space-time. Physics Letters, Section A: General, Atomic and Solid State Physics, 273(3), 149-152. View this article in WRRO
- Existence of stable hairy black holes in su(2) Einstein-Yang-Mills theory with a negative cosmological constant. CLASSICAL QUANT GRAV, 16(6), 1963-1978. View this article in WRRO
- Existence theorems for hairy black holes in su(N) Einstein-Yang-Mills theories. J MATH PHYS, 39(9), 4849-4873. View this article in WRRO
- Decoherent scattering of light particles in a D-brane background. MOD PHYS LETT A, 13(4), 303-319. View this article in WRRO
- Quantum decoherence in a four-dimensional black hole background. MOD PHYS LETT A, 12(4), 243-256. View this article in WRRO
- Dilatonic black holes in higher curvature string gravity.. Phys Rev D Part Fields, 54(8), 5049-5058. View this article in WRRO
- Aspects of hairy black holes in spontaneously broken Einstein-Yang-Mills systems: Stability analysis and entropy considerations.. Phys Rev D Part Fields, 53(6), 3190-3214. View this article in WRRO
- INSTABILITY OF HAIRY BLACK-HOLES IN SPONTANEOUSLY BROKEN EINSTEIN-YANG-MILLS-HIGGS SYSTEMS. PHYS LETT B, 352(3-4), 242-246. View this article in WRRO
- Mode-sum prescription for renormalized expectation values for a charged quantum scalar field on a charged black hole. Physical Review D, 111(4).
- Some Addition Theorems for Spin-Weighted Spherical Harmonics. Universe, 10(12), 461-461.
- Quantum-corrected anti–de Sitter spacetime. Physical Review D, 110(12).
- Equivalence of the adiabatic expansion and Hadamard renormalization for a charged scalar field. Physical Review D, 107(2).
- Dyons and dyonic black holes insu(N)Einstein-Yang-Mills theory in anti–de Sitter spacetime. Physical Review D, 93(6). View this article in WRRO
- Vacuum polarization on the brane. Physical Review D, 92(8). View this article in WRRO
- Rotating quantum states. Phys. Lett. B, 734 (2014), 296-301. View this article in WRRO
- On the existence of dyons and dyonic black holes in Einstein-Yang-Mills
theory. View this article in WRRO
- Kermions: quantization of fermions on Kerr space-time. Phys.Rev.D, 87, 064027. View this article in WRRO
- Characterizing asymptotically anti-de Sitter black holes with abundant
stable gauge field hair. View this article in WRRO
- Stability of black holes in Einstein-charged scalar field theory in a
cavity. Phys. Rev. D, 92, 124047. View this article in WRRO
- Hadamard renormalized scalar field theory on anti–de Sitter spacetime. Physical Review D, 91(4). View this article in WRRO
Chapters
- Hawking Radiation from Higher-Dimensional Black Holes View this article in WRRO
- Primordial Black Holes, SpringerBriefs in Physics (pp. 51-81). Springer Berlin Heidelberg
- Hawking Radiation and Black Hole Evaporation, SpringerBriefs in Physics (pp. 27-50). Springer Berlin Heidelberg
- Conclusions, SpringerBriefs in Physics (pp. 101-102). Springer Berlin Heidelberg
- Black Holes in General Relativity, SpringerBriefs in Physics (pp. 11-26). Springer Berlin Heidelberg
- Black Holes and Low Scale Quantum Gravity, SpringerBriefs in Physics (pp. 93-100). Springer Berlin Heidelberg
- Black Hole Formation in High Energy Particle Collisions, SpringerBriefs in Physics (pp. 83-92). Springer Berlin Heidelberg
- Classical Yang-Mills Black Hole Hair in Anti-de Sitter Space In Papantonopoulos E (Ed.) (pp. 49-87). View this article in WRRO
- INFINITELY COLOURED BLACK HOLES, The Ninth Marcel Grossmann Meeting (pp. 1626-1627). World Scientific Publishing Company
- Exact solutions in quantum field theory under rotation In Becattini F, Liao J & Lisa M (Ed.), Strongly Interacting Matter Under Rotation (pp. 95-135). Springer View this article in WRRO
Conference proceedings papers
- Einstein-Charged Scalar Field Theory: Black Hole Solutions and Their Stability (pp 69-74) View this article in WRRO
- A Menagerie of Hairy Black Holes (pp 39-46) View this article in WRRO
- Quantum corrections in thermal states of fermions on anti-de Sitter space-time. TIM17 PHYSICS CONFERENCE View this article in WRRO
- Massless rotating fermions inside a cylinder. TIM14 PHYSICS CONFERENCE - PHYSICS WITHOUT FRONTIERS View this article in WRRO
- Micro black holes in the laboratory. International Journal of Modern Physics E(Supplement 2) (pp 7-7) View this article in WRRO
- Is there classical super-radiance on Kerr-Newman-anti-de Sitter black holes?. INTERNATIONAL JOURNAL OF MODERN PHYSICS A, Vol. 17(20) (pp 2782-2782)
- Dirac fermions on an anti-de Sitter background. AIP Conf. Proc., Vol. 1634 (pp 40) View this article in WRRO
- Fermions on adS View this article in WRRO
- Kermions View this article in WRRO
- Black holes, TeV-scale gravity and the LHC View this article in WRRO
- Scalar field Hadamard renormalisation in $AdS_{n}$. Proceedings of the Thirteenth Marcel Grossman Meeting on General
Relativity, pp. 1959-1961 View this article in WRRO
- Vacuum polarisation on the brane for a higher dimensional black hole
spacetime View this article in WRRO
- Rotating fermions View this article in WRRO
- Production and evaporation of Planck scale black holes at the LHC View this article in WRRO
- Hawking radiation from rotating brane black holes View this article in WRRO
- Classical and thermodynamical aspects of black holes with conformally
coupled scalar field hair View this article in WRRO
Preprints
- Renormalized charged scalar current on a Reissner-Nordstrom black hole
in the presence of charge superradiance.
- Nonminimal coupling, quantum scalar field stress-energy tensor and
energy conditions on global anti-de Sitter space-time.
- Quantum scalar field theory on equal-angular-momenta Myers-Perry-AdS
black holes.
- Quantum fermion superradiance and vacuum ambiguities on charged black holes, arXiv.
- Some addition theorems for spin-weighted spherical harmonics.
- Mode-sum prescription for renormalized expectation values for a charged
quantum scalar field on a charged black hole.
- Quantum-corrected anti-de Sitter space-time.
- Renormalized stress-energy tensor on global anti-de Sitter space-time with Robin boundary conditions, arXiv.
- Superradiance and quantum states on black hole space-times, arXiv.
- Charge superradiance on charged BTZ black holes.
- On the equivalence of the adiabatic expansion and Hadamard
renormalization for a charged scalar field.
- Vacuum polarization on three-dimensional anti-de Sitter space-time with
Robin boundary conditions.
- Quantization of a charged scalar field on a charged black hole
background.
- Vortical Effects for Free Fermions on Anti-De Sitter Space-Time, arXiv.
- Vacuum polarization on topological black holes with Robin boundary
conditions, arXiv.
- Quantum superradiance on static black hole space-times, arXiv.
- Quantum field theory on global anti-de Sitter space-time with Robin
boundary conditions, arXiv.
- Hadamard parametrix of the Feynman Green's function of a
five-dimensional charged scalar field, arXiv.
- Hadamard renormalization for a charged scalar field, arXiv.
- Exact solutions in quantum field theory under rotation, arXiv.
- Vacuum polarization on topological black holes, arXiv.
- Analysis of scalar and fermion quantum field theory on anti-de Sitter
space-time, arXiv.
- Quantum corrections in thermal states of fermions on anti-de Sitter
space-time, arXiv.
- Thermal expectation values of fermions on anti-de Sitter space-time, arXiv.
- Black holes with ${mathfrak {su}}(N)$ gauge field hair and
superconducting horizons, arXiv.
- Effect of scalar field mass on gravitating charged scalar solitons and
black holes in a cavity, arXiv.
- Solitons and hairy black holes in Einstein-non-Abelian-Proca theory in
anti-de Sitter space-time, arXiv.
- Stability of gravitating charged-scalar solitons in a cavity, arXiv.
- Instability of sphaleron black holes in asymptotically anti-de Sitter
space-time, arXiv.
- Vacuum for a massless quantum scalar field outside a collapsing shell in
anti-de Sitter space-time, arXiv.
- Rotating fermions inside a cylindrical boundary, arXiv.
- Dyons and dyonic black holes in ${mathfrak {su}}(N)$
Einstein-Yang-Mills theory in anti-de Sitter space-time, arXiv.
- Einstein-charged scalar field theory: black hole solutions and their
stability, arXiv.
- Topological black holes in ${mathfrak {su}}(N)$ Einstein-Yang-Mills
theory with a negative cosmological constant, arXiv.
- A menagerie of hairy black holes, arXiv.
- On the stability of dyons and dyonic black holes in Einstein-Yang-Mills
theory, arXiv.
- Vacuum polarization on the brane, arXiv.
- Black hole solutions in Einstein-charged scalar field theory, arXiv.
- Stability of black holes in Einstein-charged scalar field theory in a
cavity, arXiv.
- Renormalised fermion vacuum expectation values on anti-de Sitter
space-time, arXiv.
- Massless rotating fermions inside a cylinder, arXiv.
- On the stability of soliton and hairy black hole solutions of
${mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological
constant, arXiv.
- The global rotating scalar field vacuum on anti-de Sitter space-time, arXiv.
- Hadamard renormalized scalar field theory on anti-de Sitter space-time, arXiv.
- Dirac fermions on an anti-de Sitter background, arXiv.
- Hawking Radiation from Higher-Dimensional Black Holes, arXiv.
- Rotating quantum states, arXiv.
- Fermions on adS, arXiv.
- Kermions, arXiv.
- Scalar field Hadamard renormalisation in $AdS_{n}$, arXiv.
- Vacuum polarisation on the brane for a higher dimensional black hole
spacetime, arXiv.
- Rotating fermions, arXiv.
- Production and evaporation of Planck scale black holes at the LHC, arXiv.
- On the existence of dyons and dyonic black holes in Einstein-Yang-Mills
theory, arXiv.
- Kermions: quantization of fermions on Kerr space-time, arXiv.
- Characterizing asymptotically anti-de Sitter black holes with abundant
stable gauge field hair, arXiv.
- Micro black holes in the laboratory, arXiv.
- Hawking emission from quantum gravity black holes, arXiv.
- Higher-dimensional solitons and black holes with a non-minimally coupled
scalar field, arXiv.
- Angular profile of emission of non-zero spin fields from a
higher-dimensional black hole, arXiv.
- On the existence of soliton and hairy black hole solutions of su(N)
Einstein-Yang-Mills theory with a negative cosmological constant, arXiv.
- Bulk emission of scalars by a rotating black hole, arXiv.
- Classical Yang-Mills black hole hair in anti-de Sitter space, arXiv.
- Vacuum polarization for lukewarm black holes, arXiv.
- Soliton and black hole solutions of su(N) Einstein-Yang-Mills theory in
anti-de Sitter space, arXiv.
- Abundant stable gauge field hair for black holes in anti-de Sitter space, arXiv.
- Neutrino telescope modelling of Lorentz invariance violation in
oscillations of atmospheric neutrinos, arXiv.
- Some general properties of the renormalized stress-energy tensor for
static quantum states on (n+1)-dimensional spherically symmetric black holes, arXiv.
- Brane Decay of a (4+n)-Dimensional Rotating Black Hole. III: spin-1/2
particles, arXiv.
- Brane Decay of a (4+n)-Dimensional Rotating Black Hole. II: spin-1
particles, arXiv.
- Brane decay of a (4+n)-dimensional rotating black hole: spin-0 particles, arXiv.
- Lorentz and CPT Invariance Violation In High-Energy Neutrinos, arXiv.
- Thermodynamics of de Sitter black holes with a conformally coupled
scalar field, arXiv.
- Conformally coupled scalar solitons and black holes with negative
cosmological constant, arXiv.
- Dressing a black hole with non-minimally coupled scalar field hair, arXiv.
- Probing quantum decoherence in atmospheric neutrino oscillations with a
neutrino telescope, arXiv.
- Probing Quantum Decoherence with High-Energy Neutrinos, arXiv.
- Static axially symmetric solutions of Einstein-Yang-Mills equations with
a negative cosmological constant: black hole solutions, arXiv.
- Instability of a four-dimensional de Sitter black hole with a
conformally coupled scalar field, arXiv.
- On the existence of conformally coupled scalar field hair for black
holes in (anti-)de Sitter space, arXiv.
- On the linear stability of solitons and hairy black holes with a
negative cosmological constant: the even-parity sector, arXiv.
- On classical super-radiance in Kerr-Newman-anti-de Sitter black holes, arXiv.
- On the linear stability of solitons and hairy black holes with a
negative cosmological constant: the odd-parity sector, arXiv.
- Renormalized black hole entropy in anti-de Sitter space via the "brick
wall" method, arXiv.
- Information Erasure and the Generalized Second Law of Black Hole
Thermodynamics, arXiv.
- D-particle Recoil Space Times and "Glueball" Masses, arXiv.
- Divergence of a quantum thermal state on Kerr space-time, arXiv.
- Monopole Black Hole Skyrmions, arXiv.
- The renormalized stress tensor in Kerr space-time: general results, arXiv.
- Do stringy corrections stabilize coloured black holes?, arXiv.
- Logarithmic Operators Fold D branes into AdS_3, arXiv.
- Infinitely Coloured Black Holes, arXiv.
- Existence of stable hairy black holes in su(2) Einstein-Yang-Mills
theory with a negative cosmological constant, arXiv.
- Existence Theorems for Hairy Black Holes in su(N) Einstein-Yang-Mills
theories, arXiv.
- Decoherent Scattering of Light Particles in a D-Brane Background, arXiv.
- Dilatonic Black Holes in Higher-Curvature String Gravity II: Linear
Stability, arXiv.
- Quantum Decoherence in a Four-Dimensional Black Hole Background, arXiv.
- Dilatonic Black Holes in Higher Curvature String Gravity, arXiv.
- Aspects of hairy black holes in spontaneously-broken Einstein-Yang-Mills
systems: Stability analysis and Entropy considerations, arXiv.
- Instability of hairy black holes in spontaneously-broken
Einstein-Yang-Mills-Higgs systems, arXiv.
- Hadamard renormalization for a charged scalar field. Classical and Quantum Gravity. View this article in WRRO
- Research group
-
Analysis
- Grants
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Past grants, as Principal Investigator
Higher dimensional scalar hairy black holes Nuffield Past grants, as Coinvestigator
STFC Consortium: Fundamental Physics - Lancaster-Manchester-Sheffield STFC STFC Consolidated Grant Renewal STFC Particle Physics: From the Early Universe to the Large Hadron Collider STFC Testing New Physics with Data from Particle Physics and Cosmology PPARC
- Teaching interests
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My main teaching interests are:
- Differential equations
- Mathematical physics
- Career development skills
- Teaching mathematics to engineering students
- Supervising MMath projects
- Teaching activities
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MAS222 Differential Equations MAS140 Mathematics (Chemicals) MAS151 Civil Engineering Mathematics MAS152 Essential Mathematical Skills and Techniques MAS153 Mathematics (Materials) MAS156 Mathematics (Electrical and Aerospace) MAS161 General Engineering Mathematics MAS410 Analytical Dynamics and Classical Field Theory MAS413 Analytical Dynamics and Classical Field Theory MAS6431 Analytical Dynamics and Classical Field Theory