Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Fedor Manin
Affiliation:

University of California, Santa Barbara
Date:

Thu, 27/05/2021 - 18:30 - 20:00 Please note the time.

The seminar is virtual via Zoom. If you are interested in participating, please contact Stephan Stadler (stadler

A closed $n$-manifold is \emph{scalable} if it has

asymptotically maximally efficient self-maps: $O(d^{1/n})$-Lipschitz maps

of degree $d$, for infinitely many $d$. For example, spheres and tori are

scalable, but surfaces of higher genus are not. Simply connected manifolds

that don't have a cohomological obstruction to scalability are called

\emph{formal}, an idea introduced by Sullivan. In joint work with

Berdnikov, we show that certain formal spaces are nevertheless not

scalable, and give several equivalent conditions for scalability. For just

one example, $(CP 2)^{\#3}$ is scalable but

$(CP 2)^{\#4}$ is not.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3050