Many cellular functions rely on the ability of cells to alter their shape. At the cell-membrane level, shape changes are driven by forces which, regulated by specific proteins, alter the membrane curvature through structural alterations. We will study theoretically the fluid mechanics of a cell membrane—modelled as a two-dimensional fluid layer—including a trans-membrane protein. In the absence of flows, the membrane shape is determined by a balance between Laplace pressure and bending rigidity. The presence of flows in the membrane fluid alters this picture: viscous forces stemming from the flow alter the membrane shape. This intertwinement between flows and shape may reveal novel, physical features, which we plan to study. The strong points of this internship are: Scientific publications will be aimed at the best scientific journals The student will acquire valuable skills, such as proficiency in Python, learning and mastering of the finite-element method, and others, which will be highly beneficial for his/her future scientific career. - The cross-disciplinary character of this internship, bridging between theoretical physics, differential geometry, experimental physics and biology, will offer numerous directions for future developments of the project. See https://sites.google.com/site/michelecastellana/internship-proposals for more details.