AbstractConsider the action of GL_d(Z) on the d-dimensional torus R^d/Z^d. Given a probability measure on GL_d(Z) and a point on the torus, a random walk is defined. In this talk, I will report some recent progress about the equidistribution of such random walks. More precisely, I will talk about quantitative results under the assumption that the acting group has semisimple Zariski closure. Thi...
AbstractRecently, Dervan-Legendre considered the valuative criterion of polarized varieties. We will study the valuative stability and show that it is an open condition. We would like to study the valuative criterion for the Donaldson's J-equation. Motivated by the beta-invariant of Dervan-Legendre, we introduce a notion, the so-called valuative J-stability and prove that J-stability implies va...
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