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.




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).





Algebraic geometry.







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).