Bollettino settimanale
Settimana 04/07/2022 - 08/07/2022
Seminari
Universitá degli studi di Roma ”Tor Vergata”
Dipartimento di Matematica
TOPOLOGY GEOMETRY
Date: 14 JULY 2022
Schedule: Start 15:30 - Rome Time
Where: Room 1101 ”D'Antoni”
Speaker: Andrea Marino (Universitá degli studi di Roma ”Tor Vergata”)
Title: Manifold calculus
Abstract: The aim of the talk is to give an overview of both algebraic
techniques and geometric ideas behind the manifold calculus of Goodwillie-Weiss. It is a powerful technique that can be used,
among others, to approximate spaces of knots with configuration spaces.
The framework is the following. Suppose X is a presheaf of spaces over M, and assume the restrictions X(U) → X(V) are homotopy
equivalences whenever the inclusion V→U is a (sort of) homotopy equivalence. Can we determine the homotopy type of X(M) from the
homotopy type of X on small disks? The answer is: yes, if its “Taylor Tower” converges! We will see how the cubical formalism helps
us defining the derivatives of such a presheaf, its polynomial degree and its Taylor approximation. The convergence of such approximation
relies on connectivity estimates for some maps. Here geometry comes into the picture. Since we can’t go through actual proofs, we will
show some nice geometric ideas that comes up in the theory.
If time permits, we will apply the machinery to the space of knots in dimension 4 and higher. Together with some (deep) formality results,
such technique yields the rational cohomology of knot spaces.
Organizing Committee: Paolo Salvatore (mail to)
Further Info: Click here
Streaming Link (MS Teams):
Eventi
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