L^2-theory and Spectral analysis of complex Laplacians
Student No.:50
Time:Mon/Wed 10:10-12:00, 2014-07-07 ~ 2014-07-23
Instructor:Siqi Fu  [Rutgers University-Camden]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2014-7-7
Ending Date:2014-7-23



In this course, we study L^2-theory of the Cauchy-Riemann operator and spectral properties of the complex Laplacian, as well as their applications to problems in mathematical physics and complex algebraic geometry. Our focus will be on the interplay between spectral behavior of the \bar\partial-Neumann Laplacian and geometry of the underlying complex manifold.





Familiarity with undergraduate level real analysis, complex analysis, and differential equations.





I will not follow any particular textbook. Lecture notes will be distributed. Course material will be drawn from the following texts: 


[1] An introduction to complex analysis in several complex variables (Third edition), by L.~H\"{o}rmander, Elsevier, 1991.


[2] Partial differential equations in several complex varialbes, by So-Chin Chen and Mei-Chi Shaw, AMS/IP, 2001.


[3] Complex analytic and algebraic geometry, by J.-P. Demailly, available online at the author’s website.

[4] Lectures on the L^2-Sobolev theory of the \bar\partial-Neumann problem, by Emil J. Straube, European Mathematical Society, 2010.