A Hyperelliptic Statistics on Moduli Spaces of vector bundles

In this talk, we will discuss the distribution of the $\mathbb{F}_{q}$-rational points on the various moduli spaces of vector bundles while taking a large family of hyperelliptic curves as the probability space with the uniform probability measure. This is based on joint work with Dr. Arijit Dey and Dr. Anirban Mukhopadhyay.\\

Reference: [1] Statistics of Moduli Space of Vector Bundles, Dey A., Dey S., and  A. Mukhopadhyay, Bull.Sci.Math, Vol 151 (2019), 13-33.\\
https://doi.org/10.1016/j.bulsci.2018.12.003

[2] Statistics of Moduli Spaces of vector bundles over hyperelliptic curves\\
https://arxiv.org/pdf/2409.10558