Canonical Kaehler Metrics and Stability of Algebraic Varieties
Explore canonical Kähler metrics, algebraic variety stability, and the Yau-Tian-Donaldson conjecture in complex geometry. Delve into Kähler manifolds, curvature, and pluripotential theory with recent progress and applications.
Hyper-Kähler Manifolds - Part 2
Explore advanced properties of hyper-Kähler manifolds, focusing on 4-dimensional cases and their topological characterization in relation to K3 surfaces and abelian surfaces.
Filtered Ends and Bochner Hartogs Dichotomy on Complete Kahler Manifolds
Explore filtered ends and Bochner Hartogs dichotomy on complete Kahler manifolds, examining relationships between generalized ends and first compactly supported cohomology.
Perverse Sheaves on Varieties with Large Fundamental Group
Explore perverse sheaves on Kähler manifolds, focusing on a generalization of the Singer-Hopf conjecture and its proof using Shafarevich conjecture ideas. Joint work with Donu Arapura presented.
Mixed Hodge Structures on Cohomology Jump Ideals
Explore mixed Hodge structures on cohomology jump ideals in representation varieties, extending Goldman and Millson's work to non-compact Kähler manifolds and variations of mixed Hodge structures.
Kähler Manifolds with Curvature Bounded Below
Explore Kähler manifolds with curvature bounded below, covering Yau's uniformization conjecture, compactification of manifolds, and Gromov-Hausdorff limits in this advanced mathematical survey.
Hyperkähler Manifolds: An Introduction - Part 4.1
Explore advanced concepts in complex geometry, focusing on Hyperkähler manifolds and their properties in this comprehensive mathematical lecture.
Hyperkähler Manifolds: An Introduction - Part 4.2
Explore advanced concepts of Hyperkähler manifolds with expert Elham IZADI, delving into complex geometric structures and their applications in mathematics and physics.
Hyperkähler Manifolds: An Introduction - Part 3.2
Explore advanced concepts of Hyperkähler manifolds, delving into complex geometric structures and their applications in mathematics and theoretical physics.
Hyperkähler Manifolds: An Introduction - Part 3.1
Explore advanced concepts in complex geometry, focusing on Hyperkähler manifolds and their properties in this in-depth mathematical lecture by Elham IZADI.
Holomorphic Discs of Negative Maslov Index and Extended Deformations in Mirror Symmetry
Explore holomorphic discs of negative Maslov index and their impact on mirror symmetry, focusing on extended deformations of Landau-Ginzburg models and family Floer theory in complex geometry.
Geometric Quantization of General Kähler Manifolds
Explore geometric quantization on Kähler manifolds, examining compatible constructions of function quantization, Hilbert space structure, and Kähler structure dependence in symplectic manifolds.
Calabi Problem in Generalized Kahler Geometry
Explores generalized Kahler structures, their connection to Kahler manifolds with holomorphic Poisson structures, and presents an approach to the Calabi problem in this context, with focus on toric complex Poisson varieties.
Canonical Metrics on Holomorphic Bundles
Explore canonical metrics on holomorphic bundles with renowned mathematician Shing-Tung Yau, delving into advanced geometric analysis and complex differential geometry.
Geometric Quantization of General Kahler Manifolds
Explore geometric quantization on Kähler phase spaces, examining function quantization, Hilbert space structure, and Kähler structure dependence. Investigate curvature's impact on quantization.
On the Automorphisms of Compact Kähler Manifolds
Explore automorphisms of compact Kähler manifolds with Tien-Cuong Dinh in this advanced mathematics conference talk, delving into complex geometry and dynamical systems.
Hodge Theory and Lagrangian Fibrations in Holomorphic Symplectic Manifolds
Explore Hodge theory and Lagrangian fibrations in holomorphic symplectic manifolds. Delve into conjectures, isomorphisms, and decomposition theorems in this advanced mathematical discourse.
Duality Between the Pseudoeffective and the Movable Cone on a Projective Manifold
Explore duality between pseudoeffective and movable cones on projective manifolds, including recent developments and connections to non-Archimedean Calabi-Yau theorem.
Kahler-Einstein Metrics on Fano Manifolds - ICBS 2024
Explore Kahler-Einstein metrics on Fano manifolds, bridging differential and algebraic geometry through singularity formations and recent advancements in the field.
Categorification of Lagrangian Floer Theory and Its Relation to Various Mathematics
Explore categorification of Lagrangian Floer theory and its connections to diverse mathematical fields with renowned mathematician Kenji Fukaya.
Special Holonomy and Geometric Structures on Complex Manifolds
Explore stability of critical points in self dual abelian YMH energy on Kähler manifolds. Delve into special geometric structures, complex geometry, and their connections to physics and symplectic geometry.