Completions of Period Maps
Explore the extension of period maps to compact Moishezon varieties, examining global structures and applications to moduli spaces. Insights from Hodge theory and complex geometry.
On the P=W Conjecture I
Exploration of the P=W conjecture for character varieties, its mirror version in Fano mirror symmetry, and applications to Hodge theory of Landau-Ginzburg models. Discusses recent developments and ongoing research in the field.
Differential Equations and Mixed Hodge Structures
Explores asymptotic Hodge theory, focusing on period-theoretic aspects through examples. Discusses motivic Gamma functions and their role in encoding invariants of variations of Hodge structures on P^1.
The P=W Conjecture in Genus Two and the Hodge Numbers of O'Grady 10
Exploration of moduli of sheaves, perverse filtrations, and the P=W conjecture in genus two curves, with insights on Betti and Hodge numbers of O'Grady 10 variety.
Hodge-Theoretic Aspects of Mirror Symmetry
Explores mirror symmetry for Fano varieties through Hodge theory, discussing Hodge diamond rotation, Katzarkov--Kontsevich--Pantev conjectures, and the mirror P=W conjecture in relation to mixed Hodge structures.
Tame Geometry and Hodge Theory II
Explores applications of tame geometry in Hodge theory, covering algebraization results, tameness of period maps, functional transcendence, and atypical intersection conjectures in complex algebraic geometry.
Old and New Birational Invariants
Explore new birational invariants combining Hodge theory and Symplectic Geometry in this advanced mathematics lecture by Ludmil Katzarkov.
Applications of O-minimality to Hodge Theory - Lecture 6
Explore advanced concepts in o-minimality and their applications to Hodge Theory in this graduate-level lecture by Jacob Tsimerman from the University of Toronto.
Applications of O-minimality to Hodge Theory - Lecture 1
Explore o-minimality's applications in Hodge Theory, delving into advanced mathematical concepts and their interconnections in this graduate-level lecture by Jacob Tsimerman.
Hodge Theory for the Conservativity Conjecture
Explore Hodge theory's application to the conservativity conjecture in algebraic geometry and number theory with Joseph Ayoub's insightful lecture.
A Parallel Reality Look at Generalized Geometry
Explore generalized geometries and related "Hodge theory" through a fresh perspective, building on classical works by Donaldson and Simpson in this advanced mathematics seminar.
Hodge Theory and Some Questions About 2x2 Matrices
Explore Hodge theory and intriguing questions about 2x2 matrices in this advanced mathematical lecture by Daniel Litt from the University of Toronto.
Brauer Groups, Twisted Derived Categories, and Hodge Theory
Explore recent developments in Brauer group theory, examining the period-index problem through derived categories, Hodge theory, and enumerative geometry methods.
Hidden Structures on de Rham Cohomology of p-adic Analytic Varieties
Explore hidden structures in de Rham cohomology of p-adic analytic varieties, including Hodge filtration, Frobenius, and monodromy in mixed characteristic local fields.
Heights on Curves and Limits of Hodge Structures
Explore the connection between Néron-Tate heights on smooth curves and biextension heights of limit mixed Hodge structures, with implications for computing Beilinson-Bloch heights in higher dimensions.
Hodge Theory for Poisson Varieties and Nonperturbative Quantization
Explore Hodge theory for Poisson varieties and nonperturbative quantization, focusing on K-theory and mixed Hodge structures to simplify complex calculations in deformation quantization.
Higgs Bundles, Convex Cocompact Subgroups of SU(1,n), and Slodowy Slices
Explore Higgs bundles, SU(1,n) subgroups, and Slodowy slices. Discover connections between stable Higgs bundles and holonomy groups, focusing on SU(1,n) representations and complex hyperbolic manifolds.
Birational and Singularity Invariants from Non-Commutative Hodge Theory
Explore new additive invariants of smooth projective varieties called Hodge atoms, their applications to birational equivalence, and novel singularity invariants in algebraic geometry.
Billiards, Arithmetic and Hodge Theory
Explore connections between billiard paths, cusps, curves, heights, and spectral gaps in polygons, encountering chaos and decidability issues in 7 and 12-sided shapes.
A Conjectural Reciprocity Law for Realizations of Motives
Explore a conjectural reciprocity law connecting realizations of motives, drawing parallels to classical number theory and expanding on Hodge theory's comparison isomorphisms.
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.