Isotrivial Lagrangian Fibrations of Compact Hyper-Kähler Manifolds
Explore a geometria de fibrações lagrangianas isotriviais em variedades hiperkähler compactas, incluindo tricotomia baseada na dimensão de Kodaira e busca por novos tipos de deformação.
A Construction of Apéry Constants from Landau Ginzberg Models
Explores construction of Apéry constants from Landau-Ginzberg models, linking quantum differential equations of Fano threefolds to mirror symmetry and geometric higher normal functions.
Periods, Shafarevich Maps and Applications - Nodal Surfaces and Coding Theory
Explore nodal surfaces and coding theory in K3 geometry. Learn about period maps, Torelli theorem, and binary codes in relation to polarized nodal K3 surfaces and their components.
Comparing Geometric and Hodge-Theoretic Compactifications I
Explores compactifications of moduli spaces for abelian varieties and K3 surfaces, comparing geometric and Hodge-theoretic approaches. Discusses recent work on stable K3 surfaces and recognizable divisors.
Comparing Geometric and Hodge-Theoretic Compactifications II
Explores compactifications of moduli spaces for abelian varieties and K3 surfaces, focusing on geometric interpretations and connections to Hodge theory and polyhedral decompositions.
On the P=W Conjecture II
Exploration of the mirror P=W conjecture, its evidence in low dimensions, and potential verification methods using Lagrangian torus fibrations. Discusses work with Katzarkov-Przyjalkowski and Katzarkov-Pantev.
The Mirror Clemens-Schmid Sequence
Explore a four-term exact sequence in cohomology, its relation to filtrations, and a proposed mirror to the Clemens-Schmid sequence, with applications in K3 surface settings.
On the Geometry of Hyperkähler Manifolds
Explore hyperkähler manifolds, their properties, and examples. Delve into deformation types, moduli spaces of stable sheaves, and the birational geometry of K3-type manifolds with symplectic actions.
Moduli of Bundles in Low Genus, Coble Hypersurfaces and Degeneracy Loci
Explore the geometry of moduli spaces for semistable bundles, focusing on Coble hypersurfaces and their connections to Abelian varieties, K3 surfaces, and cubic fourfolds.
Hodge Structures in 8-Dimensional Homotopy Hopf Manifolds
Explore Hodge structures on 8-dimensional homotopy Hopf manifolds, examining connections between these structures and K3 surfaces, with implications for Homological Mirror Symmetry.
Twistor Spaces and Compact Manifolds Admitting Kähler and Non-Kähler Structures
Explore twistor spaces and compact manifolds with dual Kähler and non-Kähler structures. Discover historical examples and new findings in higher dimensions using quaternion twistor spaces of hyperkähler manifolds.
Empty Real Plane Sextic Curves
Explore K3-surfaces, complex sextic curves, and real plane sextics through arithmetic and homological types. Gain insights into equivariant equisingular deformation classification.
The Dual Lagrangian Fibrations of Compact Hyper-Kähler Manifolds
Explore dual Lagrangian fibrations of compact hyper-Kähler manifolds, focusing on construction, duality, and topological mirror symmetry in higher-dimensional generalizations of K3 surfaces.
Moduli of Curves and Moduli of Sheaves - Relationships and Correspondences
Explore relationships between moduli spaces of curves, maps, and sheaves, from GW/DT correspondence to connections with K3 surfaces and abelian varieties moduli.
Exotic Calabi-Yau Metric and Holomorphic Fibration
Explore complete Calabi-Yau metrics, from historical developments to recent constructions on C^3, with insights into collapsing metrics on Calabi-Yau 3-folds.
Locally Symmetric Varieties with Moduli Interpretation
Explore complex algebraic geometry, focusing on realizing moduli spaces as locally symmetric varieties through Hodge theory. Survey existing results and examine Calabi-Yau manifolds with complex hyperbolic ball periods.
Modularity in String Theory and Moonshine - Lecture 3
Explore advanced concepts in string theory, focusing on modularity and moonshine phenomena, with expert insights from Roberto Volpato in this in-depth lecture.
Modularity in String Theory and Moonshine - Lecture 2
Explore advanced concepts in string theory, focusing on modularity and its connections to moonshine phenomena in mathematics and theoretical physics.
The Geometric Disposition of Diophantine Equations
Explore the fascinating world of Diophantine equations through geometric perspectives, focusing on rational curves, K3 surfaces, and systems of equations in this engaging mathematical lecture.
Degeneration, Geometry and Duality in String Theory
Explore generalised T-dualities in string theory, focusing on type I' and IIA duality, SYZ interpretation of mirror symmetry, and geometric duals of strong-coupling phenomena.