Friday, July 26, 2019 — 1:30 PM EDT

Hongdi Huang, Department of Pure Mathematics, University of Waterloo

"The Zariski Cancellation Problem"

Let k be an algebraically closed field. The classical Zariski Cancellation Problem for Affine Spaces asks whether the affine space An is cancellative: if V is an affine k -variety such that V × A1 = An+1∼nk kk, does it follow that V = Ak? Equivalently, if A is an affine k -algebra such that A[X] is isomorphicto the polynomial ring k[X1,...,Xn+1], does it follow that A is isomorphic to k[X1,...,Xn]? Ring theoretically, one can ask more generally for R some specific algebras, when does R[t] = S[t] imply that R and S are isomorphic as algebras? In this talk, we will introduce some useful tools to approach this problem and some known results by far.

MC 5403

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