SEMINARIO DI MATEMATICA
ore
15.00
Scuola Normale
Superiore
Pisa
(Aula
Tonelli)
Brent
Doran
ETH
Zurigo
Terrà
un seminario dal titolo:
“A
little taste of arithmetic geometric topology”
Abstract:
Topologists
developed powerful tools in the twentieth century with a focus on the
theory of manifolds. However, classical questions long solved in
topology, via fairly sophisticated techniques, have analogs which are
still open in algebraic geometry -- which, despite motivating dreams and
conjectures, lacks the precise analogs of those techniques. To cite
two simple concrete instances: (1) the cancellation problem, i.e., if X x
A^1 = A^n, then what is X, and (2) a theory of vector bundles via
classifying spaces, both have clean, complete topological stories.
We explore the rough question of what issues in algebraic geometry are
essentially topological, versus those which require hard geometry and
arithmetic, by illustrating some instances where A^1-homotopic thinking
(or ``motivic homotopy") clarifies matters. As an application, we
discuss the question "what is a sphere over Z", in a way that Heinz Hopf
would likely have appreciated.
Tutti gli interessati
sono invitati a partecipare.
Classe
di Scienze