|DATE||September 21 (Mon), 2020|
|HOST||Bhamidi, S.S Sreedhar|
|INSTITUTE||Tata Institute Of Fundamental Research|
|TITLE||[GS_M_3W] Three W's Seminar: Motivic homotopy theory - an invitation|
Since its inception in the foundational work of Morel and Voevodsky in the 1990's, motivic (or A^1)-homotopy theory has provided a systematic framework to successfully adapt several techniques of algebraic topology to the realm of algebraic geometry by having the affine line play the role of the unit interval. I will describe a heuristic, which explains how quadratic forms naturally come into picture while trying to import techniques from topology into algebraic geometry. If time permits, I will give some examples of classical results from algebraic topology and algebraic geometry and their quadratic enrichments. The talk will not assume any prior acquaintance with motivic homotopy theory.