Sung-Yeon Kim, Proper holomorphic maps between bounded symmetric domains

In this talk, we study the rigidity of proper holomorphic maps f: Ω→Ω‘​​ between irreducible bounded symmetric domains Ω​​ and Ω‘​​. First, we will define the moduli maps induced by f​​. This moduli maps are CR maps between real orbits in flag maniflods. If the rank difference is small, i.e., 2 ≤ rank(Ω‘)< 2 rank(Ω)-1​​, then there exists a moduli map which preserves the VMRT structures on the real orbits. Using this property, we will show that f: Ω → Ω‘​​ is a holomorphic totally geodesic isometric embedding with respect to Kobayashi metrics for certain pairs (Ω, Ω‘)​​. This is a joint work with N. Mok and A. Seo.