Ananya Pal to speak 'On Embedding of Linear Hypersurfaces and the Zariski Cancellation Problem'

On December 3, 2025, Ananya Pal, Research Fellow at theLaboratory on Algebraic Transformation Groups, will deliver a report 'On Embedding of Linear Hypersurfaces and the Zariski Cancellation Problem'.

Abstract:

In this talk we shall give a brief overview and address some recent developments on the above two problems.We will exhibit several families of hypersurfaces in the polynomial ring D:=k[X1,...,Xm,Y,Z,T] over an arbitrary field k defined by the linear polynomials of the form :

                        H:=a(X1,...,Xm)Y-F(X1,...,Xm,Z,T)

satisfying the Abhyankar–Sathaye Conjecture on the Epimorphism/Embedding Problem. For instance, we will show that when the characteristic of the field k is zero, F is a polynomial in Z and T only and H defines a hyperplane (i.e., the affine variety defined by H is an affine space), then H is a coordinate in D along with X1,X2,...,Xm. Our results also yield new infinite family of non-isomorphic counterexamples in positive characteristic to the Zariski Cancellation Problem.              

This talk is based on joint works with Neena Gupta and Parnashree Ghosh.

Start time: 18:00

Venue: 11 Pokrovsky Bulvar