Abstract In this talk we discuss a generalized Lax equivalence theory for the compressible Navier-Stokes system: convergence = stability + consistency. First, we introduce the concept of consistent approximation representing the (energy/entropy) stability and consistency of suitable numerical solutions. Then, by passing to the limit we obtain a dissipative weak solution with the only informatio...
Abstract A generalised pair is roughly a pair together with a nef divisor on a birational model. The theory of generalized pairs plays an important role in various aspects of birational geometry, such as the proof of the Borisov-Alexeev-Borisov conjecture. In this talk, I will discuss our recent works on the Kodaira vanishing theorem and the Kawamata-Viehweg vanishing theorem for lc generalized...