Robert Ghrist - Laplacians and Network Sheaves
Explore cellular sheaves, Laplacians, and network dynamics in algebraic topology. Learn about sheaf cohomology computation and applications in decentralized methods.
Introduction to Higgs Bundles - Lecture 1
Explore complex geometric concepts in Higgs bundles, including Riemann surfaces, theorems, and constructions. Gain insights into advanced mathematical topics through examples, exercises, and proofs.
Applications of O-minimality to Hodge Theory - Lecture 4
Explore infinitesimal thickening, definable spaces, and cell decomposition in o-minimality, with applications to Hodge theory and Abelian shields.
Applications of O-minimality to Hodge Theory - Lecture 2
Explore o-minimality's applications to Hodge Theory, covering definable spaces, fundamental domains, and Hodge metrics in this advanced graduate-level lecture.
Kato-Usui Type Extension of General Period Map
Explore Kato-Usui theory for extending non-classical period maps, its applications, and potential future directions in algebraic geometry and Hodge theory.
The Geometric Andre-Grothendieck Period Conjecture
Explore complex algebraic varieties, period integrals, and the Ax-Schanuel conjecture. Delve into transcendence theory of period maps and the Andre-Grothendieck period conjecture's functional version.
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.
Torelli Action on SU(n) Representation Varieties of Projective Curves
Explore Torelli group action on SU(n) representation varieties, its nontriviality in degree 6 cohomology, and implications for moduli of semistable bundles with trivial determinant.
Extension Data of Global Families of Mixed Hodge Structures - Applications to Shafarevich Conjecture
Extension data analysis in mixed Hodge structures: capturing global family invariants and proving Shafarevich's Conjecture in the nilpotent case through monodromy and level 1-2 extensions.
Algebraicity of the Hodge Locus in Polarized Variations of Hodge Structure
Explore algebraicity of Hodge locus in polarized variations of Hodge structure, discussing Weil's observation, Cattani-Deligne-Kaplan's proof, and recent developments in this field of algebraic geometry.
Hodge Theory, Higgs Bundles on Moduli Spaces of Manifolds and Hyperbolicity II
Explores Hodge theory, Higgs bundles, and their applications to moduli spaces and hyperbolicity, focusing on complex geometry and variation of Hodge structures.
Period Mappings at Infinity - Recent Developments II
Explores recent advancements in Hodge theory, focusing on asymptotic properties of period maps and their applications to moduli spaces beyond classical cases of ppav and K3s.
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.
Volumes of Definable Sets in O Minimal Expansions and Affine GAGA Theorems
Explore o-minimal methods in algebraic geometry, focusing on volume estimates for definable sets and their application to affine GAGA theorems, with implications for Hodge theory.
Periods and Moduli of Elliptic Surfaces I
Explore the derivative of period maps for Kaehler elliptic surfaces, examining the relationship with j-invariants and proving a generic Torelli theorem for simple elliptic surfaces.
Period Mappings at Infinity - Recent Developments I
Explores recent advancements in Hodge theory, focusing on asymptotic properties of period maps and their applications to moduli spaces beyond classical cases like ppav and K3s.
A Guide to Variations of Mixed Hodge Structure - Generalities and Examples
Explore mixed Hodge structures, their variations, and computational methods using global monodromy and iterated integrals. Illustrates concepts with the elliptic KZB variation over the universal elliptic curve.
Hodge Theory, Higgs Bundles on Moduli Spaces of Manifolds and Hyperbolicity I
Explores connections between Hodge theory, Higgs bundles, and moduli spaces, focusing on geometric properties of log spaces and variations of Hodge structures in complex manifolds.
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.
Stratifications in the Moduli Space of Stable Surfaces
Explore stratifications in stable surface moduli spaces, focusing on boundary surfaces and Hodge-theoretic approaches. Illustrated with examples and visuals from collaborative research.
Compactifications of Moduli — Geometry vs. Hodge Theory
Exploration of geometric and Hodge theoretic approaches to compactifying moduli spaces in algebraic geometry, with focus on classical cases and H and I-surfaces.