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Speaker:
Fedor Manin
Zugehörigkeit:
Ohio State University
Datum:
Fre, 22/06/2018 - 14:00 - 15:00
Location:
MPIM Lecture Hall
Parent event:
Seminar on Algebra, Geometry and Physics 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.
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