Extensions in MHM and Hain's Biextension Line Bundle - Part 2
Explores biextension line bundles, their extensions, and algebraic structures. Presents a formula for Q-line bundles, building on Hain and Pearlstein's work on normal functions and complex manifolds.
Filtered Ends and Bochner Hartogs Dichotomy on Complete Kahler Manifolds
Explore filtered ends and Bochner Hartogs dichotomy on complete Kahler manifolds, examining relationships between generalized ends and first compactly supported cohomology.
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.
Top Weight Cohomology of M_g
Explore the top-graded weight filtration on open moduli spaces, with applications to exponential growth in H^{4g-6}(M_g, Q) dimensions, disproving previous conjectures.
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.
Mixed Hodge Structures Attached to Hybrid Landau–Ginzburg Models
Explores mixed Hodge structures in Landau-Ginzburg models, focusing on functorial behavior and a new spectral sequence relating decomposed functions, with applications in mirror symmetry.
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.
The Cohomology of Shimura Varieties with Torsion Coefficients and Applications
Explore Shimura varieties' cohomology with torsion coefficients and its applications in advanced mathematics, presented by Ana Caraiani.
Ofer Gabber- Bounding the Torsion in the L-adic Cohomology of Smooth Projective Varieties Without
Explore advanced mathematical concepts in l-adic cohomology, focusing on torsion bounds in smooth projective varieties, presented by renowned mathematician Ofer Gabber.
String Topology of Finite Groups of Lie Type
Explore string topology's role in understanding cohomology of finite Lie-type groups, connecting to loop spaces and algebraic geometry. Gain insights into recent developments in this mathematical field.
Higher Topological Complexity of Seifert Fibered Manifolds
Explore LS-category and topological complexity of Seifert fibered manifolds, examining lower bounds for higher TC using cohomology class weights and deriving TC_n ranges.
Algebraic Geometry - Lecture 17
Explore advanced concepts in algebraic geometry, focusing on complex mathematical structures and their applications in modern mathematics and theoretical physics.
Algebraic Geometry - Lecture 18
Explore advanced concepts in algebraic geometry, focusing on complex mathematical structures and their applications in modern mathematics and theoretical physics.
Algebraic Geometry - Lecture 14
Explore advanced concepts in algebraic geometry, focusing on complex mathematical structures and their applications in modern mathematics and theoretical physics.
Algebraic Geometry - Lecture 12
Explore advanced concepts in algebraic geometry, focusing on complex mathematical structures and their applications in modern mathematics and theoretical physics.
Tautological Rings of Moduli Spaces of Curves - Lecture 3
Explore advanced concepts in algebraic geometry, focusing on tautological rings and their relation to moduli spaces of curves in this in-depth mathematical lecture.
ICTP-IGAP Seminar on Algebraic Geometry - Representations of the Diagonal for Moduli Spaces of Sheaves
Explore representations of the diagonal for moduli spaces of sheaves, focusing on cohomology, Chow rings, and Lie algebra actions. Gain insights into algebraic geometry and holomorphic symplectic geometry.
Topology - Lecture 12
Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
Cohomology of Stacks of Shtukas
Explore advanced algebraic geometry concepts, focusing on cohomology of shtuka stacks, with insights from Cong Xue's research in this specialized mathematical field.
P=W via H_2
Exploration of Lie algebra H_2 and its action on cohomology of moduli spaces, connecting natural filtrations and tautological operations to unify mathematical concepts.
Felix Klein Lectures 2020: Quiver Moduli and Applications
Explore quiver moduli spaces' topology, geometry, and cohomology. Discover applications in Gromov-Witten and Donaldson-Thomas theory through wall-crossing techniques in advanced algebraic geometry.