Jihoon Sohn

I earned my Ph.D. in Mathematics (thesis title: Volumes of Hyperbolic Truncated Tetrahedra) under the supervision of Professor Francis Bonahon from the University of Southern California. My research areas are deep learning, statistical analysis, natural language processing (NLP), and hyperbolic geometry. I use machine learning and statistical techniques to analyze and predict the mathematical patterns of real-world problems.

My mathematical interest lies in three-dimensional hyperbolic geometry and quantum topology. Specifically, my research focuses on the geometric reasoning of algebraic function for the volume of a hyperbolic (truncated) tetrahedron, where the formula originates from quantum topology (Volume Conjecture). In my thesis, I generalized a concept of the tetrahedron and found the extension of the existing volume formula to the domain of generalized tetrahedron. For more information, visit here.

As for machine learning, I am interested in the knowledge graph, non-Euclidean embedding, and graph representation. My recent project developed a new hyperbolic knowledge graph embedding model that better represents data's hierarchical and chronological properties than Euclidean neural networks. For more information about this or other machine learning and statistics projects, visit here.

At USC, I have taught several graduate and undergraduate level courses, including Mathematical Foundations of Statistical Learning Theory (Graduate), Introduction to Mathematical Statistics (Graduate), Linear Algebra and Linear Differential Equations, and Calculus III (student evaluations).