For my Ph.D. thesis, I have been looking at some aspects of two-dimensional vesicles. A complete list of my
publications can be found here.
Biological vesicles exhibit a variety of shapes as a function of the osmotic pressure difference and the
membrane semiflexibility. There occurs distinct classes of shapes separated by continuous phase transition. This
problem has been the topic of much study over the past couple of decades. My research for my Ph.D. thesis has been
concentrated on understanding the full features of the two-dimensional
vesicle problem. We have investigated both self-intersecting and self-avoiding classes of vesicles through a
variety of analytic and numerical problems.
For my Masters thesis, we proposed and studied a structural model for microtubules. Microtubules, which are
cylindrical structures found inside the cell, provide structural support and help in transport and cell division.
They exhibit a phenomenon called dynamical instability in which the length of the microtubule oscillates rapidly
through polymerization and depolymerization of the constituent tubulin dimers. We attempt to understand this
phenomenon through a structural cap model.