Changho Han (한창호)

Research Interests (for experts):
My research is primarily in algebraic geometry. In particular, I am mainly interested in geometric and arithmetic properties of moduli spaces of varieties (such as birational geometry, compactifications, period maps, and rational points), (enriched) enumerative problems, linear series on varieties, quadric ranks of embedded projective varieties, and syzygies of projective varieties.

See the Publications and Preprints tab for the list of my papers.

<For non-experts> What's algebraic geometry (and moduli spaces?):
Algebraic geometry originated in the study of shapes defined by zero sets of polynomials, i.e., algebraic varieties. Since functions can be approximated by polynomials, problems in other subjects such as differential geometry, number theory, mathematical physics, statistics, and geometric optimization, can be modeled by problems in algebraic geometry. I am interested in finding geometric properties of such shapes and how they change as coefficients of the underlying polynomials vary. More precisely, I am interested in problems arising from the classification of projective varieties: remarkably, it suffices to investigate a moduli space M, which is an algebraic variety that parameterizes certain collections of projective varieties of interest. Moreover, a map from a space V to M corresponds to a family of objects parameterized by V. For example, as a zero set of polynomial equations, such a family parametrized by V corresponds to the case when coefficients of polynomials are functions on V instead of being fixed numbers. In this way, M not only gives ways to understand individual objects, but also naturally gives ways to understand families of objects.

My work focuses on the geometry and arithmetic of moduli spaces that parameterizes projective varieties, particularly moduli spaces of curves and surfaces. Some of my projects involve producing explicit geometric and arithmetic descriptions of moduli spaces in various settings. The other projects instead focus on understanding invariants of curves and how they vary in special families.

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