Details
1112512
University of Warwick
06/07/2026
2 Months
36.5 hours per week, Monday-Friday. Part time hours may be accommodated upon discussion
Not Applicable
Pay
£13.75
£1.66
Description
Role
This 8-week summer internship offers an undergraduate student the opportunity to undertake a pre-defined research project within the Engineering and Physical Sciences disciplines. The intern will work under the guidance of an academic supervisor, gaining hands-on research experience while contributing to an ongoing or exploratory project. The programme also provides opportunities to connect with peers and disseminate findings via Student Research Opportunities.
Project: Inequalities concerning Additive energies via physical methods
Supervisor: Akshat Mudgal (akshat.mudgal@warwick.ac.uk)
Department: Mathematics Institute
Let G be an abelian group, and let A_1,...,A_k be finite sets in G. One is often interested in studying solutions to symmetric linear equations of the form x_1 + ... + x_k = y_1 + ... + y_k, with x_i,y_i being elements of A_i. We call this number of solutions E(A_1,...,A_k). It is natural to ask whether this inhomogeneous count E(A_1,...,A_k) can be controlled by its homogeneous variants E(A_1,...,A_1), ..., E(A_k,...,A_k). When G is an abelian group, this can be done via Fourier analysis and Holder's inequality. These methods do not extend to the non-abelian setting. In this project, we are interested in studying and proving such inequalities without using Fourier methods and relying instead on purely combinatorial techniques. This would help us generalise these results to the setting of non-abelian groups. This problem already exhibits interesting connections to linear optimisation type problems, so this would also be a nice relationship to explore.
Duties and responsibilities
• Undertake a structured, pre-defined research project under the supervision of an academic lead.
• Conduct literature reviews, data collection, analysis, and/or experimental work as appropriate.
• Participate in regular meetings with the academic supervisor to discuss progress and receive feedback.
• Engage with the wider undergraduate research community through URSS activities and events.
• Maintain accurate records of research activities and outcomes.
• Prepare and present research findings through Student Research Opportunities (e.g. presentations, posters, or reports).
• Complete two surveys (one before the internship start, one after the internship ends) for the internship funder.
• Adhere to relevant research, health and safety, and ethical guidelines.
Skills and experience
• Current undergraduate student between either their 2nd and 3rd year or 3rd and 4th year with Home fee status, studying towards a degree in Engineering or a Physical Sciences discipline at the time of the internship. Undergraduates with overseas fee status, who are between 1st and 2nd year, or who have just finished their final year are unfortunately not eligible for this funding.
• Able to commit to the full duration of the 8-week internship.
• Interest in research and willingness to engage with new concepts and methodologies.
• Good organisational and time management skills.
• Ability to work both independently and as part of a team.
• No prior research experience or additional qualifications required.
Location
Campus
Additional information
Job closing date - Midnight 25/06/26