Heat Kernels on Metric Measure Spaces with Regular Volume Growth
1 Introduction
1.1 Heat kernel in Rn
1.2 Heat kernels on Riemannian manifolds
1.3 Heat kernels of fractional powers of Laplacian
1.4 Heat kernels on fractal spaces
1.5 Summary of examples
2 Abstract heat kernels
2.1 Basic definitions
2.2 The Dirichlet form
2.3 Identifying φ in the non-local case
2.4 Volume of balls
3 Besov spaces
3.1Besov spaces in IRn
3.2 Besov spaces in a metric measure space
3.3 Embedding of Besov spaces into HSlder spaces
4 The energy domain
4.1 A local case
4.2 Non-local case
4.3 Subordinated heat kernel
4.4 Bessel potential spaces
5 The walk dimension
5.1 Intrinsic characterization of the walk dimension
5.2 Inequalities for the walk dimension
6 Two-sided estimates in the local case
6.1 The Dirichlet form in subsets
6.2 Maximum principles
6.3 A tail estimate
6.4 Identifying φ in the local case
References
A Convexity Theorem and Reduced Delzant Spaces
1 Introduction
2 Convexity of image of moment map
3 Rationality of moment polytope
4 Realizing reduced Delzant spaces
5 Classification of reduced Delzant spaces
References
Localization and some Recent Applications
1 Introduction
2 Localization
3 Mirror principle
4 Hori-Vafa formula
5 The Marifio-Vafa Conjecture
6 Two partition formula
7 Theory of topological vertex.
8 Gopakumar-Vafa conjecture and indices of elliptic operators
9 Two proofs of the ELSV formula
10 A localization proof of the Wittcn conjecture
11 Final remarks
References
Gromov-Witten Invariants of Toric Calabi-Yau Threefolds
1 Gromov-Witten invariants of Calabi-Yau 3-folds
1.1 Symplectic and algebraic Gromov-Wittcn invariants
1.2 Moduli space of stable maps
1.3 Gromov-Witten invariants of compact Calabi-Yau 3-folds
1.4Gromov-Witten invariants of noncompact Calabi-Yau 3-folds
2 Traditional algorithm in the toric case
2.1 Localization
2.2 Hodge integrals
3 Physical theory of the topological vertex
4 Mathematical theory of the topological vertex
4.1 Locally planar trivalent graph
4.2 Formal toric Calabi-Yau (FTCY) graphs
4.3 Degeneration formula
4.4 Topological vertex
4.5 Localization
4.6 Framing dependence
4.7 Combinatorial expression
4.8 Applications
4.9 Comparison
5 GW/DT correspondences and the topological vertex
Acknowledgments
References
Survey on Affine Spheres
Convergence and Collapsing Theorems in Riemannian Geometry
Geometric Transformations and Soliton Equations
Affine Integral Geometry from a Differentiable Viewpoint
Classification of Fake Projective Plan

Heat Kernels on Metric Measure Spaces with Regular Volume Growth 1 Introduction 1.1 Heat kernel in Rn 1.2 Heat kernels on Riemannian manifolds 1.3 Heat kernels of fractional powers of Laplacian 1.4 Heat kernels on fractal spaces 1.5 Summary of examples 2 Abstract heat kernels 2.1 Basic definitions 2.2 The Dirichlet form 2.3 Identifying φ in the non-local case 2.4 Volume of balls 3 Besov spaces 3.1Besov spaces in IRn 3.2 Besov spaces in a metric ...