Published on *Max-Planck-Institut für Mathematik* (http://www.mpim-bonn.mpg.de)

Posted in

- Vortrag [1]

Speaker:

Fedor Manin
Zugehörigkeit:

Ohio State University
Datum:

Fre, 2018-06-22 14:00 - 15:00 I will discuss the geometry of spaces of maps between simplyconnected finite complexes. The Lipschitz constant of a map provides a natural notion of "geometric complexity" and we study the Morse landscape of this functional, whose shape turns out to be closely controlled by rational homotopy theory. Concrete questions include: how many homotopy classes have representatives with Lipschitz constant $\leq L$ (what is the growth of $\pi_0$ of the mapping space?) Given two homotopic $L$-Lipschitz maps, how hard is to deform one to another? (does the landscape have deep valleys?) Some of this is joint work with Shmuel Weinberger, Greg Chambers, and Dominic Dotterrer.

**Links:**

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

[2] http://www.mpim-bonn.mpg.de/de/node/3444

[3] http://www.mpim-bonn.mpg.de/de/node/5312