Research Field: Algebraic Geometry
Professor: Yonghwa Cho
Research Description:
Algebraic Geometry studies geometric objects defined by polynomial equations. It is a broad field of mathematics, ranging from classical, concrete problems to modern, abstract frameworks. My research focuses on algebraic surfaces and their deformations, with particular emphasis on the interaction between classical geometry and modern homological methods.
One aspect of my research concerns how surface singularities and degenerations appear in derived categories, especially through exceptional collections and semiorthogonal decompositions. This also leads to interesting questions about (quasi-)phantom categories, whose structures are still not well understood.
More recently, I have also been studying nodal surfaces and related topics, which have deep roots in classical algebraic geometry dating back to Kummer’s work in the 19th century. The study of these topics naturally combines classical projective geometry with modern methods from homological algebra and coding theory, together with computations using computer algebra systems.