This course will give an introduction to the geometry of curves and surfaces and its use in some physical applications. The first six lectures will develop the elementary mathematical background of the subject. The last four lectures will deal with two physical applications, one to polymers and the other to membranes.
The mathematical prerequisites are elementary calculus and vectors. We will start with curves in the plane and understand the notion of curvature in this simple context. We then move to surfaces in space and distinguish between intrinsic and extrinsic curvature. This part will deal with the Gaussian curvature, parallel transport and the relation between the two. We will also look at non orientable surfaces like the Mobius strip and understand these ideas with simple paper cutting exercises.
The first physical application relates to polymers which are long chain molecules. We will touch upon the worm like chain model (WLC) of polymer elasticity. The second application is to surfaces. We will understand how the surface tension of membranes determines their shape. The basic idea of the course is to combine geometry with soft matter physics.
This summer course is meant for undergraduate and postgraduate students from science and engineering disciplines.
Schedule:
May - 17, 18, 24, 25, 31
June - 1, 7, 8, 14, 15
Time: 11.30 AM to 1.00 PM
This course will be conducted in hybrid mode (including lectures and tutorials). Students can choose either classroom or online participation. More details will be shared separately with the selected candidates.
Participants will not be provided any financial support and local hospitality for attending the course.
Registration: closed
For any queries contact us at : summer . course @ icts . res . in