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.
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.
Hecke Actions on Loops and Periods of Iterated Shimura Integrals
Exploration of Hecke actions on loops and periods of iterated Shimura integrals, focusing on SL_2(Z) and modular curves, with insights into mixed modular motives and Galois action.
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.
Hyperbolicity in Presence of a Large Local System
Explore hyperbolicity in complex algebraic varieties with Yohan Brunebarbe. Learn about Green-Griffiths and Lang conjectures, and their validity for varieties with large complex local systems.
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.
Hyperbolicity of Algebraic Varieties via Fundamental Groups
Explore hyperbolicity of algebraic varieties through fundamental groups, examining linear representations and their implications for complex quasi-projective varieties and the Green-Griffiths-Lang conjecture.
L2 Invariants of Hodge Modules and Shafarevich Morphisms
Explore L2 invariants of Hodge Modules and Shafarevich morphisms, including L2 constructible cohomology and Mixed Hodge structures, with potential topological implications of linear Shafarevich conjecture.
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.
Twistor Space for Moduli of Local Systems on Open Curves
Explore Deligne-Hitchin twistor spaces for moduli of framed local systems on open curves, examining harmonic bundles, preferred sections, and mixed twistor structures in moduli space geometry.
Homological Mirror Symmetry - Floer Homotopy Theory
Explore recent developments in Floer generalized homology groups, their applications, and ongoing research on curvature in Floer homotopy theory with expert Mohammed Abouzaid.
Homological Mirror Symmetry - Mohammed Abouzaid - Floer Homotopy Theory Pt. II
Explore recent advancements in Floer generalized homology groups, their applications, and ongoing research on curvature in this context with Mohammed Abouzaid.
Homological Mirror Symmetry - Floer Homotopy Theory
Explore recent developments in Floer generalized homology groups, their applications, and ongoing research on curvature in Floer homotopy theory with Mohammed Abouzaid.
On the Rouquier Dimension of Wrapped Fukaya Categories
Explores Rouquier dimension of wrapped Fukaya categories, linking symplectic topology to algebraic geometry through homological mirror symmetry. Discusses applications to Lagrangian intersections and Lefschetz fibrations.
Homological Mirror Symmetry for Hypersurface Singularities II
Explores graded matrix factorizations of invertible polynomials and stability conditions in homological mirror symmetry for singularities, continuing from a previous lecture.
Surface Singularities and Invariants of Their Links
Explore the connection between surface singularities and their link's topology, focusing on quantum invariants and their relation to the spectrum of Brieskorn spheres.
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.
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.
Extensions of Hodge Structure and Completions of Fundamental Groups
Explore extensions of mixed Hodge structures, unipotent and relative completions of fundamental groups, and their geometric interpretations in L-functions and motives theory.