Jordan Algebras and Complex Geometry

  Not much background will be required for that. Then some recent topics will be discussed in the second hour.

New example of Hartogs type extension phenomenon

In this talk we study results in a paper (Arxiv : 1706.01441v2)

 a connected open set V which contains supp can be extended to a holomorphic function

On the Hartogs Analyticity Theorem

On smoothly bounded domains covering finite volume manifolds

Diederich-Fornaess index and Steinness index.

- Speaker: Mr. Jihun Yum (POSTECH)

- Abstract: 

Let D be a bounded pseudoconvex domain in ℂ^n with smooth boundary. Diederich-Fornaess index DF(D) is η1 iff for all η ∈ (0, η1), there exists a defining function ρ such that -(-ρ)^η is strictly plurisubharmonic on D. Steinness index S(D) is η2 iff for all η > η2, there exist a defining function ρ and a neighborhood U of ∂D such that ρ^η is strictly plurisubharmonic on (closure{D})^c ∩ U.

We will see the relation between Diederich-Fornaess index and Steinness index on smooth Worm domains.

Poster  <---Click here

- Speaker: Prof. Andrew Zimmer (William and Mary University)

- Abstract: 

For certain classes of bounded domains we give a precise description of the automorphism group and its limit set in the boundary. For instance, for finite type pseudoconvex domains we prove: if the limit set contains at least two different points, then the automorphism group has finitely many components and is the almost direct product of a compact group and connected Lie group locally isomorphic to Aut (B_k). Further, the limit set is a smooth submanifold diffeomorphic to the sphere of dimension 2k-1. For convex domains with C^1,ε boundary we can prove a similar result. In this talk we will describe the main ideas of the proofs and discuss some applications.

- Speaker: Prof. Chong-Kyu Han (Seoul National University)

- Abstract: 

I will review first the Pfaffian system technique for overdetermined PDE systems, then present some applications.

An interesting feature of complex analysis of several variables is that for smoothly bounded domains in Cⁿ, 

n ≥ 2, function theory of the domain depends on the geometry of its boundary. In particular, whether or not the boundary contains a complex subvariety often has to be determined, mainly because it is “characteristic” for the Cauchy-Riemann equations.

I want to present my recent results in these directions.

- Speaker: Dr. Ngoc Coung Nguyen (GAIA)

- Abstract: