## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

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

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.