d-objects kinematics on smooth manifolds

Model building with intersecting D6-branes on smooth Calabi-Yau manifolds

We study intersecting D6-branes in Calabi-Yau manifolds that are smooth hypersurfaces in weighted projective spaces. We develop the techniques for calculating intersection numbers between special Lagrangian sub-manifolds defined as fixed loci of anti-holomorphic involutions. We present global Pati-Salam and MSSM-like models that are supersymmetric up to a decoupled hidden sector.

Exotic Structures on smooth 4-manifolds

A short survey of exotic smooth structutes on 4-manifolds is given with a special emphasis on the corresponding cork structures. Along the way we discuss some of the more recent results in this direction, obtained jointly with R.Matveyev, B.Ozbagci, C.Karakurt and K.Yasui.

AdS中引力子区域的全息与运动学空间

Holography and Kinematic Space for Gravitational Sub-regions in AdS

利用运动学空间中的测地线（PEE线）覆盖AdS子区域，提出Crofton公式计算子区域边界面积，并构建全息张量网络实现表面态对应和广义纠缠楔。

D-branes and synthetic/$C^{\infty}$-algebraic symplectic/calibrated geometry, I: Lemma on a finite algebraicness property of smooth maps from Azumaya/matrix manifolds

We lay down an elementary yet fundamental lemma concerning a finite algebraicness property of a smooth map from an Azumaya/matrix manifold with a fundamental module to a smooth manifold. This gives us a starting point to build a synthetic (synonymously, $C^{\infty}$-algebraic) symplectic geometry and calibrated geometry that are both tailored to and guided by D-brane phenomena in string theory and along the line of our previous works D(11.1) (arXiv:1406.0929 [math.DG]) and D(11.2) (arXiv:1412.0771 [hep-th]).