Homological Mirror Symmetry for Theta Divisors
Exploring homological mirror symmetry for theta divisors in principally polarized abelian varieties, with insights from ongoing research in complex moduli and SYZ fibrations.
On the Presentability of Artin Differentiable Stacks
Explore the global quotient presentability of Artin stacks in smooth settings, delving into advanced mathematical concepts in differential geometry and algebraic topology.
Lagrangian Intersections in Phase Tropical Hypersurfaces
Explore phase tropical hypersurfaces, their relation to complex hypersurfaces, and combinatorial analogs of Lagrangian spheres and thimbles. Discuss connections to mirror matrix factorization categories.
Gromov-Hausdorff Convergence of Filtered A Infinity Categories
Explore Floer homology's dependence on Hamiltonian isotopy, its multiplicative structure, and connections to homological Mirror symmetry in formal deformation theory.
Holomorphic Floer Theory, Quantum Wave Functions and Resurgence
Explore holomorphic Floer theory, exponential integrals, and resurgence in algebraic geometry. Discover connections to quantum wave functions and infinite-dimensional applications.
Derived Categories and Motives of Moduli Spaces of Vector Bundles on Curves
Explore derived categories and motives of moduli spaces of vector bundles on curves, their relationships, and recent developments in algebraic geometry.
Stability Structures in Holomorphic Morse-Novikov Theory
Explore complex symplectic manifolds, Floer theory, and Morse-Novikov theory. Delve into analytic questions of convergence and generalization to almost-complex cases in this advanced mathematical lecture.
Basic Remarks on Lagrangian Submanifolds of Hyper-Kähler Manifolds
Explore properties of Lagrangian subvarieties in hyper-Kähler manifolds, focusing on their interaction with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.
Topological Invariants of Compact Singular Varieties
Explore topological invariants of compact singular varieties with José Seade from UNAM. Gain insights into advanced mathematical concepts and their applications in algebraic geometry.
Adelic Toric Varieties and Loop Groups
Explore proalgebraic spaces, adelic abelian algebraic groups, and vector bundle categories. Discover adelic loop groups, Grassmannians, and the Birkhoff-Grothendieck theorem for holomorphic bundles.
Oriented and Unitary Equivariant Bordism of Surfaces
Exploration of equivariant oriented and unitary bordism groups, focusing on torsion parts and obstruction classes for surfaces with free action. Presents key findings and non-trivial invariants.
Extensions in MHM and Hain's Biextension Line Bundle - Part 2
Explores biextension line bundles, their extensions, and algebraic structures. Presents a formula for Q-line bundles, building on Hain and Pearlstein's work on normal functions and complex manifolds.
The Nilpotent Orbit Theorem, New and Old
Explore Schmid's proof and a new approach to the nilpotent orbit theorem for polarized complex variations of Hodge structure, with insights on local monodromy.
Operations on Cyclic Complexes, Getzler-Gauss-Manin Connection, Noncommutative Crystalline Cohomology
Explore advanced algebraic concepts including cyclic complexes, Getzler-Gauss-Manin connection, and noncommutative crystalline cohomology in this in-depth mathematical lecture by Boris Tsygan.
Extensions in MHM and Hain's Biextension Line Bundle - Part 1
Explore complex manifolds, biextension line bundles, and normal functions in algebraic geometry. Discover formulas for Q-line bundle extensions and their topological invariants.
Equivariant Birational Geometry of Three-Dimensional Projective Space
Explore finite group actions on 3D projective space, focusing on G-solid cases and their G-Mori fiber spaces. Gain insights into advanced algebraic geometry concepts.
Finite Generation and K-Stability
Explore recent advances in birational geometry and their impact on K-stability, including finite generation of valuations and connections to major conjectures in algebraic geometry.
Lattice Cohomology - Part 2
Explores advanced concepts in lattice cohomology, focusing on topological and analytic aspects, their connections to singularity theory, and implications for geometric structures.
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.
Constructible Sheaves and Filtered D-Modules
Explore the Riemann-Hilbert correspondence and its p-adic analogue, connecting constructible sheaves to filtered D-modules with applications in algebraic geometry.
Hyper-Kähler Manifolds - Part 1
Explore the foundations of hyper-Kähler manifolds, their connection to K3 surfaces, and key properties in this advanced mathematics lecture by renowned expert Claire Voisin.