MMathPhys/MSc in Mathematical and Theoretical Physics Handbook (2025-26 Entry)

(alex.schekochihin@physics.ox.ac.uk)

 

Abstract:

Ordinary gases and plasmas where binary collisions between particles occur on time scales that are shorter than the time scales of collective dynamics usually hover close to Maxwellian equilibria — an expression of the thermodynamical inevitability ubiquitous in nature. What, however, happens if the collisions are infrequent, like they are in many astrophysical plasmas (and also in most gravitating kinetic systems)? The question has been on the agenda since the 1960s but in recent years, there have been a number of interesting developments that suggest a path forward, previously obscure. It turns out that the principle of maximum entropy can be applied to such systems if one treats the particle distribution function (phase-space density) itself as a random field and asks how its coarse-grained (averaged) version evolves subject to constraints imposed by (approximate) incompressibility of the phase space (encoded in a continuum of Casimir invariants). Universal equilibria emerge — they can be derived by the methods of statistical mechanics (maximising entropy), but a further challenge is to do to the resulting equilibria what Boltzmann did to Maxwell’s distribution and work out how (and why) they are achieved dynamically. This means deriving, essentially, an effective field theory for the evolution of non-Maxwellian plasmas — “collisionless collision integrals”. Under some rather restrictive assumptions, this has been done for Vlasov-Poisson (electrostatic plasmas). The student’s first task would be to learn the necessary theory that leads one to that point. From there, they will be looking over the research frontier into terra incognita. A useful research-level task would be to work out how (and whether) the existing theory can be generalised to Vlasov-Maxwell (electromagnetic) plasmas. Another would be to try some new approaches to deriving collision integrals beyond the quasilinear approximation. It is also possible that, in the course of their exploration of the subject, the student might tread onto a third path, which cannot as yet be predicted.

 

Reading:

D. Lynden-Bell, "Statistical mechanics of violent relaxation in stellar systems," Mon. Not. R. Astron. Soc. 136, 101 (1967) 

T. H. Dupree, "Theory of phase space density granulation in plasma," Phys. Fluids 15, 334 (1972) 

R. J. Ewart et al., "Collisionless relaxation of a Lynden-Bell plasma," J. Plasma Phys. 88, 925880501 (2022) 

R. J. Ewart et al., "Non-thermal particle acceleration and power-law tails via relaxation to universal Lynden-Bell equilibria," J. Plasma Phys. 89, 905890516 (2023) 

A. A. Schekochihin, "Lectures on Kinetic Theory and Magnetohydrodynamics of Plasmas”, secs 10-11 and references therein, https://www-thphys.physics.ox.ac.uk/people/AlexanderSchekochihin/KT/2015/KTLectureNotes.pdf

 

 

Abstract: 

This dissertation is related to the previous one: the relaxation of collisionless plasmas towards universal non-Maxwellian equilibria occurs because the plasma is in a turbulent state that is very different from thermal (particle) noise that underlies the relaxation of collisional systems to the local Maxwellian equilibrium. This turbulence occurs in a 6D phase space and has only recently started to be understood theoretically and probed numerically. An especially fascinating (and, it seems, highly consequential) feature of it appears to be that, due to the phenomenon of particle trapping in electric fluctuations, long-lived coherent structures can form and then engage in vigorous dynamics, interacting with each other, growing to ever-larger size at each other’s expense, and in the process stirring the plasma in a manner that pushes it towards non-Maxwellian states. In this dissertation, the student will first study the fundamental theory underlying our understanding of these structures and then, if they (the student) have sufficient energy and gain sufficient momentum while there is still time, they can attempt to construct a theory of turbulence of phase-space structures. A promising lead is that it will turn out to be linked to the theories of strong Langmuir turbulence developed in the 1970s-80s, but never finished due to impossibility at that time of testing ideas on large computers (which are now available and have yielded some intriguing new data).

 

Reading:

I. B. Bernstein et al., "Exact nonlinear plasma oscillations,” Phys. Rev. 108, 546 (1957) 

T. O’Neil, "Collisionless damping of nonlinear plasma oscillations," Phys. Fluids 8, 2255 (1965) 

I. H. Hutchinson, "Kinetic solitary electrostatic structures in collisionless plasma: phase-space holes,”, arXiv:2407.08539 (2024) 

M. L. Nastac et al., "Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence," Phys. Rev. E 109, 065210 (2024) 

A. A. Schekochihin, "Lectures on Kinetic Theory and Magnetohydrodynamics of Plasmas”, secs 8, 12 and references therein (on strong Langmuir turbulence, see references in sec. 8.6.2), https://www-thphys.physics.ox.ac.uk/people/AlexanderSchekochihin/KT/2015/KTLectureNotes.pdf

 

(henriques@maths.ox.ac.uk)

 

Abstract:

The Virasoro algebra is an important infinite dimensional Lie algebra, with a rich and fascinating representation theory. It is the universal central extension of the Lie algebra of vector fields on the circle, and plays a central important role in two-dimensional conformal field theory. The proposal will start with an investigation of Lie algebra cohomology, specifically the relation between $H^2$ and Lie algebra central extensions. Then, a specific construction called the Segal-Sugawara construction will be investigated: every representation of a so-called affine Lie algebra is automatically also a representation of the Virasoro algebra. At last, we will aim for a classification of the irreducible representations of the Virasoro algebra. An ambitious (optional) goal would be to study the so-called fusion product of representations of the Virasoro algebra, which equips the category of representations of the Virasoro algebra with the structure of a modular tensor category. (Note: initial supervision for this project may be held in groups.)

 

Pre-requisites:

B2.3 Lie Algebras

Recommended:

C2.2 Homological Algebra

C2.3 Representation Theory of Semisimple Lie Algebras

 

Reading:

Course notes: http://andreghenriques.com/Teaching/CFT-2020.pdf

A Mathematical Introduction to Conformal Field Theory, by M. Schottenloher.

V. G. Kac. Infinite-dimensional Lie algebras. Cambridge University Press.

Unitary representations of the Virasoro and super-Virasoro algebras, by P. Goddard, A. Kent, and D. Olive

Conformal Field Theory, by David Sénéechal, Philippe Francesco, and Pierre Mathieu

Representation Theory of the Virasoro Algebra, by Kenji Iohara, and Yoshiyuki Koga.

Friedan, D., Qiu, Z.A. and Shenker, S.H., 1984. Conformal invariance, unitarity and two-dimensional critical exponents. Physical Review Letters, 52, p.1575.

Wang, W., 1993. Rationality of Virasoro vertex operator algebras. International Mathematics Research Notices, 1993(7), pp.197-211.

 

 

(dancer@maths.ox.ac.uk)

 

Abstract:

This project would explore aspects of symplectic geometry, especially those related to group actions on symplectic manifolds. The project would start with a review of the basic theory of symplectic manifolds, Hamiltonian group actions and moment maps. Further topics could include all or some of the following: (i) Abelian actions, toric varieties and Delzant’s theorem. (ii) moment maps and symplectic reduction (iii) Duistermaat-Heckman theorem (iii) geometric quantisation of symplectic manifolds, in particular a detailed treatment of the case of Delzant spaces There are many examples in toric geometry that could be workedout, and quite a few details that  he candidate could fill in during an exploration of the literature. There are extensive links with convex geometry, combinatorics and even some parts of number theory.

 

Prerequisites: 

It would be helpful to take Differentiable Manifolds and C3.5 Lie Groups

 

Reading: 

V. Guillemin. Moment Maps and Combinatorial Invariants of Hamiltonian T n Spaces (Birkhauser). M. Audin. 

The Topology of Torus Actions on Symplectic Manifolds (Birkhauser).

 

 

(anton.sokolov@physics.ox.ac.uk)

 

Abstract:

Hypothetical particles called axions are one of the most popular candidates for the role of the cold dark matter, moreover axions can explain the absence of the electric dipole moment of the neutron. Possible electromagnetic signatures of axions are actively searched for in laboratory experiments and astrophysical observations. Recently, a new form of axion electrodynamics was proposed which evades many of the existing experimental searches. The goal is to study the implications of this new form of axion electrodynamics for astrophysical observations, and possibly predict novel axion signals from stars. 

 

Prerequisites: 

Electrodynamics and Field Theory, Basics of Astrophysics. 

 

Reading: 

G. Raffelt, "Stars as Laboratories for Fundamental Physics", 2) A. Caputo and G. Raffelt, "Astrophysical Axion Bounds: The 2024 Edition".

 

 

(ard.louis@physics.ox.ac.uk)

 

Abstract:

Evolution proceeds by mutations to genotypes that in turn change phenotypes (the organism). But since the number of genotypes is much larger than the number of phenotypes, concepts of genetic entropy must enter into the equations, which means methods from statistical mechanics become relevant.  In this project you will study some recent advances that use algorithmic information theory to argue for a bias towards simplicity in biology.  See, for example, the papers below:

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution, Iain G Johnston, Kamaludin Dingle, Sam F. Greenbury, Chico Q. Camargo, Jonathan P. K. Doye, Sebastian E. Ahnert, Ard A. Louis PNAS 119, e2113883119 (2022).

Bias in the arrival of variation can dominate over natural selection in Richard Dawkins’ biomorphs View ORCID Profile, Nora S. Martin, Chico Q. Camargo, Ard A. Louis doi: https://doi.org/10.1101/2023.05.24.542053 

 

Abstract:

Many models in biology, engineering and physics have a very large number of parameters. Often many of these are only known approximately. Moreover, in John von Neuman’s famous quip “with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” suggests that only a small set of these parameters are actually relevant? Could there be a fundamental theory of these complex systems that allows us to work out what the key parameters are?

 

References:

1. Transtrum, Mark K., Machta Benjamin, Brown Kevin, Daniels Bryan C., Myers Christopher R., and Sethna James P. , Perspective: Sloppiness and Emergent Theories in Physics, Biology, and Beyond, J. Chem. Phys., Volume 143, Issue 1, (2015)

2. Machta, Benjamin B., Chachra Ricky, Transtrum Mark K., and Sethna James P. , Parameter Space Compression Underlies Emergent Theories and Predictive Models, Science, Volume 342, p.604-607, (2013)

3. Gutenkunst, R. N., Waterfall J. J., Casey F. P., Brown K. S., Myers C. R., and Sethna J. P., Universally sloppy parameter sensitivities in systems biology models, PLoS Computational Biology, Volume 3, p.1871-1878, (2007)

4. Waterfall, J. J., Casey F. P., Gutenkunst R. N., Brown K. S., Myers C. R., Brouwer P. W., Elser V., and Sethna J. P. , Sloppy-model universality class and the Vandermonde matrix, Physical Review Letters, Volume 97, p.150601, (2006)

 

Abstract:

Deep neural networks (DNNs) have revolutionised machine learning. In spite of their great success, many questions remain about why they work so well. One key issue is why they generalise so well in the overparameterised regime, where classical learning theory predicts that they should heavily overfit. We have recently used concepts from Algorithmic Information Theory (AIT) to argue that that DNNs are exponentially biased towards functions with low Kolmogorov complexity. If this inductive bias reflects patterns seen in nature, then this may explain the conundrum of good generalisation in the overparameterised regime. But many questions remain, and in this project you would use a combination of theory and simulations to peer into the DNN black box, and to hopefully understand what makes them so special.

 

See http://www.physicsmeetsml.org/posts/sem 2020 06 03/ for some more background.

 

Abstract:

For many pathogens, infection-blocking immunity is transient even though immunity against severe disease (whether acquired through natural infection or vaccination) may be lifelong. The interplay between seasonal changes in HIT and loss of infection blocking immunity is therefore a critical determinant of dynamics of pandemic spread and of the characteristics of endemic equilibrium of any emerging pathogen. This project will focus on:

i. how the time of arrival of the pathogen within the seasonal cycle of transmissibility affects the initial dynamics of infection and subsequent establishment of an endemic equilibrium;

ii. how these dynamics are affected by pre-existing immunity (for example, due to exposure to related pathogens);

iii. how mass vaccination can alter these dynamics. 

We will refer to available data on SARS-CoV-2 in various settings to test and refine the hypotheses generated by these exercises.

 

 

(couzens@maths.ox.ac.uk)

 

Title: Equivariant Localization and supergravity

Abstract: Equivariant localisation is a powerful mathematical result which allows for the evaluation of integrals on a space with a symmetry using topological data of the space. It has recently been used in supergravity to compute various observables such as the on-shell action and anomalies. This thesis will review this recent topic before applying it to a new setup.

Pre-requisites: The topic uses Riemannian geometry and supersymmetry/supergravity. The student should be familiar with the basics of Riemannian geometry (metric, curvature, forms) or taking the GR1 C7.5 course and/or the Differentiable manifolds (C3.3) course. Supersymmetry and Supergravity will be learnt as a byproduct of the dissertation.

Title: Classifying supersymmetric solutions in supergravity

Abstract: Finding solutions to the Einstein equations is very difficult, they are second order non-linear equations. One method for finding solutions is to impose additional symmetries, one such symmetry is supersymmetry. Imposing that the solution preserves supersymmetry typically allows us to replace the second order PDEs with first order PDEs. We will review how this is done using G-structures and Generalised complex geometry before applying this to a new class of solutions.

Pre-requisites: The topic uses Riemannian geometry and supersymmetry/supergravity. The student should be familiar with the basics of Riemannian geometry (metric, curvature, forms) or taking the GR1 (C7.5) course and/or the Differentiable manifolds (C3.3) course. Supersymmetry and Supergravity will be learnt as a byproduct of the dissertation.

 

 

(edward.hardy@physics.ox.ac.uk)

 

Abstract: 

One of the outstanding mysteries of the Standard Model of particle physics is the absence of CP violation in the strong sector. This project involves first reviewing the origin of CP violation in gauge theories, which has a fascinating connection to non-perturbative dynamics. Possible solutions to the strong CP problem will also be studied. A two-unit project could extend to analysing a recent paper that claims (possibly erroneously) that there is in fact no strong CP problem.

 

References:

Advanced Topics in Quantum Field Theory, Shifman (widely available in libraries)

 

Abstract: Hamiltonian truncation is an approach to analysing quantum field theories in the strongly coupled regime, in which the full Hilbert space of the theory is truncated and the resulting system is studied numerically. This project will involve reviewing the existing literature and attempting to exploit machine learning techniques to obtain an optimized truncated subspace.

 

Reading:

 

 

 

 

Supervisor: Prof Fabian Essler

(fabian.essler@physics.ox.ac.uk)

Title: Heating rates in Floquet circuits

Abstract: In recent years there has been a lot of interest in simulating interacting many-particle quantum systems using superconducting circuits. Brickwall circuits naturally give rise to periodically driven (“Floquet”) circuits. These are known to heat under time evolution [1,2] und approach an infinite temperature (completely mixed) state at late times. Circuits that have a globally conserved charge are then expected to exhibit hydrodynamic behaviour. In order to study the latter using numerical methods it is necessary to have a circuit that heats fast, so that the accessible time scales suffice to detect it. The objective of the project is to investigate a simple class of two-Qbit brick wall circuits with a single conserved charge, and use the diagnostic proposed in [3] to find which circuits heat fastest.

Reading list: 

[1] A. Lazarides, A. Das and R. Moessner, Phys. Rev. E90, 012110 (2014).
[2] L. D’Alessio and M. Rigol, Phys. Rev. X 4, 041048 (2014).
[3] A. Rakcheev and A.M. Lauchli, Phys. Rev. Research 4, 043174 (2022).

 

 

(lotay@maths.ox.ac.uk)

 

 

 

(jospeh.conlon@physics.ox.ac.uk)

 

Abstract: Cosmic strings are extended 1-dimensional topological defects that have long been considered a possible element of the universe. Such strings can arise either in field theory through symmetry breaking phase transitions or as fundamental cosmic superstrings. Although cosmic strings were originally considered as a candidate for structure formation in the universe, this possibility did not survive contact with data on large-scale structure and the distribution of galaxies. However, low-tension cosmic string networks still exist as a possibility and are a speculative explanation for the origin of the ultra-low frequency gravitational waves recently observed by pulsar timing arrays. The dissertation will review the physics of cosmic strings and explore some aspect of their physics in more depth. It can be offered as either a 1- or 2-unit dissertation.

Pre-requisites: While no course is an absolute pre-requisite, a familiarity with field theory and cosmology would be very helpful.

Reading list:

As starter references, 

Cosmic Strings and Other Topological Defects, (Vilenkin + Shellard, CUP, 2000)
Cosmic Strings and Superstrings, E. Copeland and T. Kibble, arXiv:0911.1345

These should then be used as a base from which to explore the literature.

 

 

 

(julia.yeomans@physics.ox.ac.uk)

 

Abstract: 

Active systems take energy from their surroundings on a single particle level and use it to do work. This means that they naturally operate out of thermodynamic equilibrium and provide examples of non-equilibrium statistical physics. Dense active matter has many surprising properties such as active turbulence and motile topological defects, motility induced phase separation, odd viscosities and the breakdown of detailed balance. The dissertation will probe more deeply into an aspect of active materials; possible examples are spontaneous flow in confined active systems, swimming at low Reynolds number, active wetting or forces in confluent cell layers.

 

Reading: 

G Gompper et al, The 2020 motile active matter roadmap, J. Phys.: Condens. Matter 32 193001

(lots of short articles introducing active matter)

A. Doostmohammadi, J. Ignés-Mullol, J.M. Yeomans, and F. Sagués, Active nematics. Nat. Commun. 9, 3246 (2018) (for a review of active nematics)

 

 

 

 

(lionel.mason@maths.ox.ac.uk)

 

Title: Twistor theory and applications

Abstract: Twistor theory is a geometrical framework for the formulation of physical theories introduced by Roger Penrose in the 1960s.  It provides a more primitive geometry from which space-time itself emerges together with physical fields thereon using ideas from algebraic geometry and complex analysis. It traces its origins to the Klein correspondence from classical projective geometry in which the space of lines in three dimensional projective space form a four-dimensional quadric which in twistor theory is re-interpreted as Minkowski space-time.  This framework has had  many applications to mathematical physics over the years, any one of which might form the basis for a dissertation of one or two units.  

1.  The classification of integrable systems of nonlinear equations of Mathematical Physics and construction of exact solutions, see Mason \& Woodhouse, Integrability, Self-Duality and Twistor Theory, OUP Monograph, 1996.  This could be reviewed in the light of recent Chern-Simons approaches due to Costello, Witten and Yamazaki, Gauge Theory and Integrability, ICCM Not. 06, arxiv:1709.09993.

2. Applications to the construction of scattering amplitudes and correlation functions for 4d gauge and gravity theories.  A prerequisite is QFT and a general introduction to scattering amplitudes can be found in the CUP book by Elvang and Huang book available at https://arxiv.org/abs/1308.1697.  From here one could study more recent developements such as ambitwistor strings and the scattering equations, Geyer and Mason The SAGEX Review: Ambitwistor strings and amplitudes from the worldsheet, J.Phys.A 55 2022, arxiv:2203.13017 or more recent applications to the construction of cosmological and AdS correlators A new twist on spinning (A)dS correlators https://arxiv.org/abs/2408.02727.  Another approach is via twistor actions which more ambitiously connects to celestial holography, see Kmec, Mason, Ruzziconi and Sharma, S-algebra in Gauge Theory: Twistor, Spacetime and Holographic Perspectives, arxiv:2506.01888.   

 

 

(nick.jones@maths.ox.ac.uk)

 

Abstract: 

Entanglement entropy (EE) is of fundamental importance to our understanding of ground states of quantum many-body systems. The aim of this dissertation is to review some recent developments in the area of symmetry-resolved EE - the EE of a particular symmetry sector of the ground state. Directions one can take include calculations in exactly-solvable lattice models, and numerical investigation of the ground states of different symmetric Hamiltonians.

 

Prerequisites:

Part B Further Quantum Theory (or equivalent)

 

Relevant courses:

Quantum Field Theory, Random Matrix Theory.

 

Reading:

P. Calabrese and J. Cardy 2009 J. Phys. A: Math. Theor.42 504005

M. Goldstein and E. Sela 2018 Phys. Rev. Lett. 120, 200602

R. Bonsignori, P. Ruggiero and P. Calabrese 2019 J. Phys. A: Math. Theor. 52 475302

S. Fraenkel and M. Goldstein J. Stat. Mech. (2020) 033106

N. G. Jones J. Stat. Phys., 188, 28 (2022)

 

 

 

(renaud.lambiotte@maths.ox.ac.uk)

 

Abstract:

Many real-world networks are composed of directed edges that are not necessarily reciprocated. While several algorithms have been generalised to the case of directed networks, conceptual challenges, i.e. to quantify the level of hierarchy (and its impact on dynamics). In this project, we will investigate the notion of hierarchy in directed networks from different, possibly complementary viewpoints. The two main challenges will be to design embedding techniques allowing to rank nodes according to their importance, while grouping “similar nodes”, and to investigate how hierarchies impact on linear dynamics, more specifically via the non-normality of the coupling matrices.

 

Prerequisites:

Taking the course C5.4. Networks is recommended.

 

Reading list:

MacKay, Robert S., Samuel Johnson, and Benedict Sansom. "How directed is a directed network?" Royal Society open science 7.9 (2020): 201138.

Lambiotte, Renaud, and Michael T. Schaub. Modularity and Dynamics on Complex Networks. Cambridge University Press, 2021.

 

 

Title: Dynamics and structure of complex-weighted networks

Abstract: Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools of network science when the weight of edges are complex numbers. The purpose of this project will be to explore further the structure and dynamics of such complex-weighted networks. We will consider linear processes such as consensus dynamics and random walks, from which build algorithms to extract information from the systems. Relatedly, the student may consider problems where edges are equipped by linear transformation, thus going beyond rotations in two dimensions.

Reading list:

Tian, Yu, and Renaud Lambiotte. "Structural balance and random walks on complex networks with complex weights." SIAM Journal on Mathematics of Data Science 6.2 (2024): 372-399.

Tian, Yu, et al. "Matrix-weighted networks for modeling multidimensional dynamics." arXiv preprint arXiv:2410.05188 (2024).

Supervisor: Dr Seyed Faroogh Moosavian

(faroogh.moosavian@maths.ox.ac.uk)

Title: Quantum Theory of Gravity

Abstract: Quantum gravity has remained elusive for nearly a century, dating back to the earliest attempts by Pauli, Heisenberg, Rosenfeld, Bronstein, and others in the 1930s. Despite numerous efforts on many fronts, this arguably most profound challenge at the foundation of theoretical and mathematical physics has not yet yielded. In fact, it is fair to say that all existing approaches have not even managed bending this very thick rod, let alone cracking it [1, 2].
This project aims to delve into one of the most important series of papers in the history of the subject: the trilogy Quantum Theory of Gravity I, II, and III by Bryce DeWitt, a (if not the) principal architect of modern research in the field [3, 4, 5]. These papers encompass the canonical and covariant approaches to the quantization of gravitational interactions, applications of these methods, the derivation of the famous Wheeler–DeWitt equation, the problem of time, the many-worlds interpretation of quantum mechanics, the principal challenges that remain in completing the program, and much more.
Among DeWitt’s many contributions, which can be read about in [6], two stand out for their foundational importance in quantum field theory and quantum gravity alike: the de¬velopment of the background-field method, and the systematic formulation of gauge-fixing in the path integral formalism. The background-field method allows one to maintain man¬ifest gauge (and diffeomorphism) invariance while quantizing fluctuations around a fixed classical background–crucial for any sensible approach to perturbative quantum gravity. Closely related, DeWitt’s elegant and general approach to gauge fixing—via what would become known as the Faddeev–Popov procedure–originates from the very ideas developed in these papers.
Unlike most modern literature on the subject, this series is highly technical: there are no random or vague assumptions made to simplify or obscure the main challenges. The attempt is to build everything for the quantization of gravity in four spacetime dimensions from scratch. As such, the project is correspondingly demanding–certainly not for the faint of heart. Anyone interested is strongly encouraged to browse the papers in advance to get a sense of their scope and depth. If you remain interested after that, please contact me for further discussion.
For a Master’s student, the goal will be to absorb as much as possible—not necessarily by reading the entire trilogy, but by seriously engaging with its core ideas and reflecting on potential questions that might be addressed using these methods. The dissertation should include:
1.    A detailed review of one of the main topics or methods from the trilogy;
2.    An exploration of one question that can be pursued using that reviewed topic or method—this could either be a question that has already appeared in the literature, or, if the student is ambitious, something entirely new.
The choice in (2) depends on whether the student would like to complete a one-unit or two-unit dissertation.
Please Notice: If your main goal is to perform quick computations, publish a paper immediately, or engage with the latest hot and mainstream developments, then this project may not align with your interests. Its purpose is to build a strong and lasting foundation in the subject, one that you can draw upon in your future studies, if you are inclined to pursue it further. For clarity, there is no supersymmetric content in this project.

Reading list:
[1]    R. P. Feynman, F. B. Morinigo, W. G. Wagner, B. Hatfield, J. Preskill and K. S. Thorne, Feynman Lectures on Gravitation. Addison–Wesley, Jun, 1995. 1
[2]    R. P. Woodard, How Far Are We from the Quantum Theory of Gravity?, Rept. Prog. Phys. 72 (Jul, 2009) 126002, [0907.4238]. 1
[3]    B. S. DeWitt, Quantum Theory of Gravity. I. The Canonical Theory, Phys. Rev. 160 (Aug, 1967) 1113–1148. 1
[4]    B. S. DeWitt, Quantum Theory of Gravity. II. The Manifestly Covariant Theory, Phys. Rev. 162 (Oct, 1967) 1195–1239. 1
[5]    B. S. DeWitt, Quantum Theory of Gravity. III. Applications of the Covariant Theory, Phys. Rev. 162 (Oct, 1967) 1239–1256. 1
[6]    S. M. Christensen, ed., Quantum Theory of Gravity, Essays in Honor of the 60th Birthday of Bryce C DeWitt. CRC Press, 1984. 1

Supervisor: Dr Thomas Spieksma

(thomas.spieksma@physics.ox.ac.uk)

Title: Interactions of black holes crossing through active galactic nuclei

Abstract: Extreme-mass-ratio inspirals (EMRIs) are expected to be key sources for the future space-based gravitational-wave observatory LISA, yet their formation channels are poorly understood. One promising scenario involves stellar-mass black holes being captured by active galactic nuclei (AGN). These captures occur at large distances from the central black hole, and their subsequent evolution must be modelled to predict when and how they enter the LISA sensitivity band. In this project, the student will study the interaction of the captured black hole with the AGN, and determine the expected orbital parameters (such as inclination and eccentricity) by the time the system reaches the relativistic regime.

For relevant literature and further information, please contact Dr Spieksma directly.