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Nonsmooth differential geometry

Lecturer: 
Nicola Gigli
Course Type: 
PhD Course
Academic Year: 
2017-2018
Period: 
October-March
Duration: 
60 h
Description: 
1. First order calculus on metric measure spaces:
  • Sobolev functions on metric measure spaces
  • Lp-normed modules
  • differential calculus on metric measure spaces
  • maps of bounded deformation and their differential
 
2. Second order calculus on RCD spaces:
  • definition of RCD spaces
  • the space W2,2 and Hessian of a function
  • covariant and exterior differentiation
  • aspects of cohomology
  • if time permits: applications to geometry

Lecture Notes: You can find weekly updated lecture notes, written by Enrico Pasqualetto, by clicking this link.


 

Location: 
A-133

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