# Mathematics Algebra and Topology Seminar - Eoin Mackall

This event is in the past.

**Date:**November 9, 2022

**Time:**1:30 p.m. - 2:30 p.m.

**Category:**Seminar

**Speaker:** Eoin Mackall, University of Maryland, College Park

**Title:** Naive $mathbb{A}^1$-homotopy equivalences and theorems of Whitehead and Zariski

**Absract:** A naive A^{1}-homotopy between morphisms f,g from a variety X to a variety Y is a cycle on (XxA^{1})xY whose support is finite and surjective over XxA^{1} and whose fibers over 0 and 1 are the graphs of f and g respectively. Using this notion of naive A^{1}-homotopy, one can define naive A^{1}-homotopy equivalences of varieties. In this talk, we’ll discuss how an analog of a theorem of Whitehead can be used to show that there are no nontrivial A^{1}-homotopy equivalences between smooth projective varieties.

## Contact

Department of Mathematics

3135772479

math@wayne.edu