Program
Algebraic Microlocal Analysis
Student No.:50
Time:Wed 10:10-12:00/Fri. 15:10-17:00, 2015-11-25 ~ 2015-12-30 (except for public holidays)
Instructor:Francois-Xavier Machu  [Tsinghua University]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2015-11-25
Ending Date:2015-12-30

 

 The Class on December 12 is canceled.

 

 
Description:

 

In the sixties, people were used to work with various spaces of generalized functions constructed with the tools of functional analysis. Sato’s construction of hyperfunctions in 59-60 is at the opposite of this practice: he uses purely algebraic tools and complex analysis. The importance of Sato’s definition is twofold: first it is purely algebraic and second it highlights the link between real and complex geometry. He introduced the notion of microlocalization functor.

 

 

We first recall the notion of D-modules quickly and those derived category to tackle the notion of microlocalization of sheaves and the Riemann-Hilbert correspondence (if the time permits it).

 

 

Prerequisite:

 

Algebraic geometry.

 

 

 

Reference:

 

 

M. Kashiwara, on the holonomic system of linear differential equations, Inven. Math. 49 p. 121-135, (1978).

 

 

M. Kashiwara and P. Schapira Microlocal study of sheaves, Asterique 128 Soc. Math. France (1985).