Glimpses of Global Theory of Surfaces

Course: Glimpses of global theory of surfaces [ July 10 to July 12th, 2026]

Course description: After setting up the necessary tools from multivariable calculus succinctly, we intend to discuss some beautiful results from global extrinsic geometry of surfaces. This includes theorems of Liebmann and Hopf and culminates in Alexandroff's theorem on surfaces.

Instructor: Aprameyan Parthasarathy and Parthasarathy Krishnan

Course topics: 1. Inverse and implicit function theorems, regular values.

                           2. Integration and surface integrals

                           3. Divergence theorem and Minkowski integral identities

                           4. Principal, Gaussian and mean curvatures

                           5. Liebmann's theorem on surfaces

                           6. Why are soap bubbles round ? - Alexandroff's theorem

Deadline for application: 30th June, 2026, 4:00 PM.

The list of selected candidates will be available on the website by 2nd July 2026.  

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