Maria-Carme Calderer

My research deals with partial differential equations, dynamical systems and calculus of variations. I study applications to soft matter physics and biology. Specific topics of my research include investigating how DNA arranges itself under confinement (e.g.,in the cell as well as in laboratory settings). The mathematical tools involved include calculus of variations, to determine the energy minimizing configuration of the DNA as well as topology, with the goal of understanding the knotting structure. A dynamical problem associated with DNA is the study of the process of bacterial infection by viruses. Another research topic addresses the dynamics of active matter, with the goal of understanding how cancer cells move in tissue. The dynamical models deal with fluid mechanics of non-Newtonian fluids, colloids and solid-fluid structures. The presence of electric charge often brings the coupling of the equations of fluid dynamics with the formulations by Boltzmann and Nernst -Planck of the motion of charged particles and colloids. I also have industrial collaborations, in the area of medical devices, as well as work on problems from the pharmaceutical industry. My research is funded by different programs of the National Science Foundation.