Speaker: Nidhi Gupta
Date: September 25, 2025
Affiliation: TIFR, Mumbai

Abstract: It is a classical fact that a smooth projective quadratic hypersurface over a field $k$ is rational precisely when it admits a $k$-rational point. Let $k$ be a field of characteristic 0. A theorem of Asok-Morel further shows that any smooth projective rational variety is $\mathbb{A}^1$-connected, so for smooth projective quadrics over $k$, $\mathbb{A}^1$-connectedness is governed by the existence of a $k$-rational point. In this talk, I will present an analogous characterization for affine quadrics in terms of classical invariants of the associated quadratic form. The argument draws on the study of rational curves on these hypersurfaces together with techniques from quadratic form theory. This talk is based on joint work with Dr. Chetan Balwe. <br> <br> <br>