TODAY: BASIC NOTIONS SEMINAR Thursday 29 January at 14:00 - Paul Arne Østvær (University of Milan)

[ICTP Math Section]

_*BASIC NOTIONS SEMINAR*_

Thursday 29 January at 14:00

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*Venue:* Leonardo Building - Luigi Stasi Seminar Room (In-Person)

*Speaker:* Paul Arne Østvær (University of Milan)

*Title:* Topology with Polynomials: Motivic Homotopy Theory and Affine Space

*Abstract: *Motivic homotopy theory applies ideas from topology to 
algebraic varieties by replacing continuous paths with polynomial paths 
given by the affine line. We introduce this viewpoint starting from 
intuitive notions of manifolds and varieties and explain what it means 
for a variety to be \mathbb{A}^1-contractible. In low dimensions this 
notion is rigid, but in dimension three exotic examples appear, such as 
the Koras–Russell threefolds. Motivated by the topological 
characterization of Euclidean space, we discuss a proposed motivic 
analogue for affine space using the motivic homotopy type at infinity. 
This illustrates how motivic homotopy theory provides a new notion of 
“shape” for polynomial spaces.

All are welcome to attend.

https://indico.ictp.it/event/11275/