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Statement of research interest for a Ph.D application in Quantum Gravity

Protonovich 1 / -  
Sep 13, 2023   #1
Hello everyone. I am writing a statement of research interest (SRI henceforth) and a cover letter for a Ph.D position in Dublin in the field of Quantum Gravity. I've never written a SRI and, honestly, I am not very sure how to do it, especially since I've seen that this kind of document is typical for later academic positions. There are no specific requirements or guidelines in the application other than "submit this". Summary at the end.

The next is what I've written based on Google research about SRI and several samples I've found. Again, all the material out there is for post-doc or tenure-track positions where you can already expand on your previous research achievements, so I've tried to adapt them to a kinda of blank background. Here is the statement:

Statement of Research Interest

From my earliest encounters with Quantum Mechanics and General Relativity, I've been captivated by their remarkable predictive power and their elusive compatibility. This led me to delve into Causal Set Theory and become mostly absorbed by it. In this statement , I aim to convey not only my deep-seated curiosity but also my unwavering commitment to unravel the mysteries of Quantum Gravity. I am confident that I will perfectly suit the expectations of the 'Hawking Radiation and Black Hole Entropy in Causal Set Theory' team, especially considering Supervisor's passion for entanglement entropy and cosmology, and Co-Supervisor dedication to QFT models.

Research area.

My primary research interest is in the area of Quantum Gravity and Cosmology. It is well-known that General Relativity and Quantum Mechanics are highly incompatible, while both of them yield astonishingly accurate predictions. On the other hand, gravitation at large scales requires the curvature of spacetime to either emerge at some intermediate scale or be induced by an underlying structure that already encodes that information. Since this is a paramount challenge in modern Theoretical Physics, I am more than committed to making my contributions to propel our insights on it. Furthermore, after studying the Causal Sets approach I became devoted to taking part in its successful development.

Delving into the mechanisms of Quantum Gravity through CST to further our understanding and achieve solid outcome is the general goal of my research. How to retrieve the macroscopic structure of reality from a fundamental structure following a bottom-up approach and how to connect this underlying fabric with the properties of cosmological evolution, the early stages of the universe, black holes paradoxes and the behaviour of information near its event horizon, are the central questions that fuel most of my future research plans.

Those were the seeds of my craving for CST, since it perfectly encompasses the fundamental approach and the adaptability to address these questions. Set aside, CST owns the most accurate prediction of Λ up to date. Due to their complexity, attaining satisfactory explanations for such matters requires a high dose of creativity, detailed analysis, and soft skills that result in valuable developments and worthwhile collaborations. In my methodology, I intend to combine theoretical analysis and computational simulations to in-depth explore the impact of a discrete, causal structure in the widest range of scenarios, from particle dynamics to cosmology.

Current and past research.
Since I started my college education my attention has oscillated between high-energy Physics and Gravitation. I oriented every opportunity I had to work hand-in-hand with professional scientists on these subjects, resulting in two Nuclear Physics and one General Relativity project.

Undergraduate projects.
I participated in two Nuclear Physics projects at Consejo Superior de Investigaciones Científicas, in Madrid, during my last undergraduate year. As part of my B.Sc thesis, and under the supervision of Pedro Sarriguren and Óscar Moreno, I studied the influence of nuclear deformation in the amplitude of double-beta decay with neutrino emission. By computational means, I accomplished to calculate the deformation dependence of the transition and determined the most favourable configuration for the decay to occur.

Additionally, I was granted a research internship with Eduardo Garrido to analyze three body systems in Quantum Mechanics, using numerical calculations to study the emergence of Efimov states and Borromean nuclei. We achieved to obtained the regimes in which the aforementioned states emerged and calculated their wave functions. Overall, I improved my ability to move between different theoretical schemes instead of sticking to what I was taught, and acquired fluency in computational Physics.

Master's thesis and beyond.
Once I began my M.Sc in Theoretical Physics I contacted Bert Janssen in Granada to get his supervision for a General Relativity M.Sc thesis. I aimed to delve into stationary metrics, particularly in rotating black holes, and their causal structure. We first derived stationary solutions of Eintein's Equations exploting Cartan's tetrad formalism and the Jannis-Newman algorithm. After obtaining various solutions with and without cosmological constant, I derived and scrutinize several Penrose diagrams to study the causal structure of representative spacetimes.

After my M.Sc I have kept studying different techniques and approaches of General Relativity and QFT to increase my understanding of them and enlarge my own toolkit. During these incursions, I reached Causal Set Theory and immediately captivated me, leading to self-conducted learning. During the following years I studied, among others, the Energetic Causal Sets approach of Cortês and Smolin, with whom I have had the privilege to talk regularly, the work of Dowker with Benincasa in retrieving Einstein-Hilbert action, and the research of Sorkin and Dou about black hole and entanglement entropy.

Future research directions
I envision my future research to ramify across interrelated sub-areas of Quantum Gravity and Cosmology through the lens of CST. Although my near term plan relies on which Ph.D project I joined, I expect the core of my long-term future research will lie in the mathematical foundations of Causal Set Theory and their phenomenology.

The research issues I intend to address include, among others, the following:
· Implementation of quantum-compatible dynamics for Causal Sets.
· The influence of entanglement entropy in large scale structures and the early universe,
· Dynamics of bosonic and fermionic fields in the causet, and gravity couplings,
· The Hauptvermutung, shedding light towards its resolution,
· Testable predictions to reinforce CST as a suitable theory:
◦ Signatures in the gravitational waves and neutrino backgrounds,
◦ Effects in the cross section of matter-antimatter annihilation that can solve the asymmetry problem.

Additionally, I want to emphasize my interest in building a strong network of collaborations. I am convinced that sharing ideas and knowledge and fostering cooperation is the best way to propel cutting-edge research towards significant achievements. Thus, I would relish collaborating with a variety of experts in the topics listed above. To mention a few, David Rideout for the dynamics due to his expertise in sequential growth, Fay Dowker for emergent properties due to her developments on retrieving Einstein-Hilbert action and the Lorentz invariance of causets; Smolin and Cortês because of their model with energetic constraints and their work in cosmology; and, of course, Rafael Sorkin since I would gain invaluable insights in the nature of Causal Sets.

This Ph.D program under the supervision of Supervisor and Co-Supervisor offers a unique opportunity to be formally introduced to professional Causal Sets research and begin my career as a professional scientist. Finding out the passion of Supervisor for entanglemente entropy and CST cosmology in her latest publications, as well as the expertise of Co-Supervisor in different QFT models, was immensely encouraging. I am enthused to join project and leverage this program to dig into the realm of Causal Sets.

Thank you for your time and consideration.
Best regards,

End of the statement

- Statement of research interest for a Ph.D position in Quantum Gravity,
- I open stating that my interests are well-aligned with those of the team and the (co-)supervisor of the project,
- Section talking about open questions and issues that are captivating for me and how they relate to the position,
- Section talking about the opportunities I've had to collaborate with professional scientist and how these little research in linked to Quantum Gravity,
- Section talking about my prospective plans, mentioning that my near term plans depend on the Ph.D I joined, followed by a succint list of specific topics,

- Paragraph showing my willingness to teamwork and collaborations to show my commitement with cutting-edge avancements,
- Final paragraph insisting in the alignment of my interests with those of the team and the supervisors.

Additional information and request
- This statement is 1121 words long, I've seen that it is appropriate to keep in the 600-1000 range, I ignore how to trim it.
- The audience are the supervisor and co-supervisor of the project, meaning their experts in the field and know technical terms and usual abbreviations.
- I've ommited the names for privacy.
- This document is accompanied by a cover letter where I state my willingess to provide further information about any aspect of the application, I didn't want to include it in here because I would surpass three pages, which would seem too lenghty,

- Is it appropriate to include citations? I understand its relevance once I've produced my own work and I can relate to it, but I don't know to what extent is it correct to include the papers I've familiar with.

- Any advice, commentary, and suggestion will be greatfully appreciated.
- Deadline is Friday the 15th, my apologies for such short time, I have just discovered this forum.

Thank you in advance for the attention!

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