My main research interests lie in the distribution of algebraic, rational, and integral points on algebraic varieties from the various points of view of number theory --- finiteness, non-density, effectiveness, quantitativeness, etc. All these are closely connected to one another. For instance, finiteness leads to a question of effectiveness (i.e., whether it is possible to determine all those finitely many objects under consideration explicitly) and quantitativeness (i.e., how the finite numbers vary under some involved parameters). Another research interest subject of mine is algebraic geometry --- more geometry-oriented. An example is what we can say about lower-dimensional sub-varieties of a fixed higher-dimensional variety and how we can apply the results to the study of the higher-dimensional variety, or the other way around. This looks fascinating in itself, but also has something close to do with the number-theoretical questions stated above.
number theory, distribution of algebraic, rational, and integral points on algebraic varieties, algebraic geometry, arithmetic and geometric aspects of higher-dimensional algebraic varieties