Unitemps Warwick · Coventry, United Kingdom · internship · [object Object]
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 settin