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...
Note: There is no lecture on May 3, 2022 for it's Labor Day Holiday.Abstract：The first half of the course is devoted to explaining fundamental concepts, terms, facts and tools in probability theory and stochastic analysis. Then, in the second half, we pick up some topics in stochastic partial differential equations as applications of stochastic analysis.Contents:(1) Foundations of Probability ...
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