Colloquium on Friday, October 11, at 2 pm 

Dr. Gunhee Cho from Texas State University, invited by Dr. Hee Cheol Chung, will give a colloquium talk on Friday, September 11, at 2:00 pm in Fretwell 315. 
The title and abstract of his talk are attached below.

Title. Geometry of bounded domains in C^n via Statistical models

Abstract. The family of -dimensional normal distributions reveals a distinct differential geometric structure known as the Poincaré Upper Half Plane, arising from the Fisher-Information metric. The widely applied Cramér-Rao lower bound can be understood as a reflection of the Fisher-Information metric’s decreasing nature. Furthermore, this metric’s decreasing property resonates with the differential geometric interpretation of the Schwarz-Pick lemma within the Poincaré Disk of complex analysis. In this presentation, our goal is to extend the insights from the Poincaré Disk to encompass bounded domains in C^n as statistical models, leveraging observations from normal distributions and the Schwarz-Pick lemma. By treating bounded domains as statistical models, we establish a coherence between the Bergman metric and the Fisher-Information metric, introducing a natural decreasing property. Additionally, the establishment of an equality condition of two Bergman metrics corresponds to the identification of sufficient statistics. This recent work is a collaborative effort with J. Yum.