Creative Telescoping for the Canham Model in Genus 1

Explore the powerful algorithmic method of Creative Telescoping and its applications in experimental mathematics through this 40-minute lecture by Sergey Yurkevich from the University of Vienna and Inria, Saclay. Delve into the theoretical foundations of Creative Telescoping and witness its practical application to a biological physics problem concerning biomembrane shapes. Learn how this method can automatically compute and prove recurrences for binomial sums, equality of period functions, and moments of measures. Discover the application of Creative Telescoping to the variational Helfrich problem for genus 1 biomembranes, involving the computation of surface area and volume of a Clifford torus projection using Gaussian hypergeometric functions. Gain insights into the joint work with Alin Bostan and Thomas Yu, demonstrating the monotonic increase of the rescaled ratio of these functions.

Sergey Yurkevich - Creative Telescoping for the Canham model in genus 1