May 12 event at ISI Kolkata

On 23rd July afternoon there was a program in the Platinum Jubilee Auditorium of ISI Kolkata under the May 12 initiative. There were more than 100 participants from various colleges and universities in Kolkata including Presidency College, IISER Kolkata, IACS (Indian Association for the Cultivation of Science), Kolkata University, Jadavpur University and of course students and faculty members of ISI Kolkata.

In the first half of the program there was a public lecture by Prof. Kingshook Biswas explaining the mathematical work of Maryam Mirzakhani. The title and abstract of the talk were as follows.

Title: Counting simple closed geodesics on hyperbolic surfaces, after Mirzakhani

Abstract: We describe the work of Mirzakhani on counting simple closed geodesics on hyperbolic surfaces. Mirzakhani proved an exact polynomial asymptotic for the number of simple closed geodesics of length less than L, as L tends to infinity. The proof has topological, dynamical and geometric ingredients. 

We give a brief introduction to hyperbolic geometry and the hyperbolic plane, and give a sketch of the proof of an asymptotic formula in the much simpler case of counting simple closed geodesics on a flat genus one surface (a flat torus), which illustrates the main ideas of Mirzakhani’s proof for the case of hyperbolic surfaces of genus two or higher.  

He explained Maryam’s work very nicely, using very many pictures and in a way that was as non-technical as possible. He discussed the formula for the growth of the number of simple closed geodesics of length ≤ L, the fact that a very long simple closed geodesic on a surface of genus 2 is six times more likely to be nonseparating, and hence for an arbitrary surface of genus 2 the probability that a random simple closed geodesic will cut the surface into two genus 1 pieces is  1/7. 

There was a break for tea and snacks. 

In the second half of the program the Director of the Institute Prof. Sanghamitra Bandopadhyay addressed the gathering. 

Finally there was a film screening “Secrets of the surface: The Mathematical Vision of Maryam Mirzakhani”.