My main subject is Arithmetic Invariant Theory．It studies the statistical behavior of arithmetic objects such as algebraic number fields or Mordell—Weil rank of elliptic curves. The theory interprets arithmetic objects by algebraic objects or orbits of representations of algebraic groups, and then combine with techniques of analytic number theory. I am particularly interested in those interpretation, and problems arising from classical algebraic geometry and classical invariant theory in arithmetic settings.

Keywords	Number Theory, Arithmetic Invariant Theory, Diophantine Geometry
Faculty , Department	Institute of Mathematics for Industry , Fundamental Mathematics