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.
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.
Complex Hyperbolicity and Representations of the Fundamental Group in Non-Compact Varieties
Explore complex hyperbolicity and fundamental group representations in quasi-projective varieties, blending archimedean and non-archimedean approaches to extend previous research in algebraic geometry.
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.
On Nilpotent Quotients of Quasi-Kähler Groups
Exploration of nilpotent quotients of quasi-Kähler groups, focusing on smooth complex quasi-projective manifolds and their quasi-Albanese maps, with implications for holomorphic convexity and special manifolds.
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.
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.
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.
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 - 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 - Counting Curves on Calabi-Yau Threefolds
Explore advanced mathematical concepts in counting curves on Calabi-Yau threefolds, including Grothendieck groups, Gopakumar-Vafa conjecture, and MNOP conjecture implications.
Multispectra
Explore new birational invariants in algebraic geometry with Professor Ludmil Katzarkov, delving into advanced mathematical concepts and their applications.
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.
Homological Mirror Symmetry for Hypersurface Singularities
Explore homological mirror symmetry for hypersurface singularities, covering basic definitions, Berglund-Hubsch duality, known results, and detailed examples in this advanced mathematics lecture.
Alexander Polynomials of Algebraic Links
Explore Alexander polynomials of algebraic links, their definitions, examples, and connections to algebraic geometry. Discover the relationship between plane curve singularity spectra and link polynomials.
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.