6 papers
Asymptotic expansion of induced Grassmannian Chern forms and distribution of random degeneracy sets
Turgay Bayraktar, Dan Coman, Bingxiao Liu +1
For the Grassmannian embeddings defined by the spaces , where is a positive line bundle and is a holomorphic vector bundle over a compact complex manif…
Nakano-Griffiths inequality, holomorphic Morse inequalities, and extension theorems for -concave domains
Bingxiao Liu, George Marinescu, Huan Wang
We establish a general Nakano-Griffiths inequality with boundary conditions and apply it to derive holomorphic Morse inequalities for domains satisfying analytic convexity assumpti…
Tian's theorem for Grassmannian embeddings and degeneracy sets of random sections
Turgay Bayraktar, Dan Coman, Bingxiao Liu +1
Let be a compact Kähler manifold, be a positive line bundle, and be a Hermitian holomorphic vector bundle of rank on . We prove that the pullback…
Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros
Bingxiao Liu, Dominik Zielinski
We give an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Rieman…
Toeplitz operators and zeros of square-integrable random holomorphic sections
Alexander Drewitz, Bingxiao Liu, George Marinescu
We use the theory of abstract Wiener spaces to construct a probabilistic model for Berezin-Toeplitz quantization on a complete Hermitian complex manifold endowed with a positive li…
Integral invariants for framed 3-manifolds associated to trivalent graphs possibly with self-loops
Hisatoshi Kodani, Bingxiao Liu
Bott--Cattaneo's theory defines the integral invariants for a framed rational homology 3-sphere equipped with an acyclic orthogonal local system, in terms of graph cocycles without…