## Dr. Mangala J. Narlikar Memorial Lecture

(Organised by Bhaskaracharya Pratishthana, Pune)

**Prof. Nitin Nitsure,** will deliver a lecture on **“What is curvature?”**

A straight path does not turn, while a curved path turns. Curvature is a measure of how much a path is turning. It also has a two dimensional analog. A table top is flat (it is the 2-dimensional analog of a straight line). But the surface of a ball is curved. How to measure the amount of curvature at a point of a surface?

Gauss proposed a measure for it which is named `Gaussian curvature' in his honour. In this lecture, I will explain how Gaussian curvature is defined, and how the total amount of the Gaussian curvature of a surface is related to its Euler characteristic, which comes from its global topology. This relationship is called the Gauss-Bonnet theorem.

Finally, I will describe an elementary way to obtain the curvature of a surface via geodesics, proved recently in 2019. The talk will assume some basic knowledge of calculus and matrices, at the level of 1st year BSc.

- Day and Date: Thursday, 7th March 2024
- Venue: AV Hall, Library Building, Bhaskaracharya Pratishthana, Pune.
- Time: 5:00 pm to 6:00 pm

All are cordially invited to attend the lecture.