# Seminars & Events for Department Colloquium

##### Log term of the Bergman kernel and the deformation complex for CR structures

Fefferman showed that the Bergman kernel of strictly pseudoconvex domains admit logarithmic singularity. For the case of the ball, the log term vanishes and it is conjectured that the log term vanishes only for the ball. Robin Graham proved it in 2-dimensions, while for higher dimensions, counter examples were found for domains which are not Stein. However, I still believe that the conjecture is true for domains in C^n. In this talk, I use Kuranishi's deformation complex of CR structures to determine the moduli space of the deformation of the ball (based on the works of Bland-Ducahmp) and apply the result to prove the conjecture for domains sufficiently close to the ball.

##### Regularity of area-minimizing surfaces in higher codimension: old and new

The theory of integral currents, developed by Federer and Fleming in the 60s, gives a powerful framework to solve the Plateau's problem in every dimension and codimension. The interior and boundary regularity theory for the codimension

one case is rather well understood, thanks to the work of several mathematicians in the 60es, 70es and 80es.