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.
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.
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.
On Wormholes in the Moduli Space of Surfaces
Explore wormholing phenomena in KSBA compactification of moduli space for surfaces of general type, focusing on extremal P-resolutions and open questions in the field.
Surfaces with One T-Singularity
Explore stable surfaces with specific properties, focusing on I-surfaces with T-singularities. Gain insights into Gorenstein surfaces and applications to KSBA compactification of Gieseker's moduli space.
Secondary Fan, Theta Functions, and Moduli of Calabi-Yau Pairs
Explore the conjecture on moduli space of triples, unirational components, and toric variety covers. Discover generalizations of secondary fans and universal family constructions in algebraic geometry.
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.
Atiyah Class and Sheaf Counting on Local Calabi-Yau 4 Folds
Explore Donaldson-Thomas invariants of torsion sheaves in Calabi-Yau fourfolds, examining their relation to reduced DT theory and modularity predictions for elliptic K3 surfaces.
Donaldson-Thomas and Gromov-Witten Theories - Part 10
Explore moduli spaces of algebraic curves and coherent sheaves, their invariants, and connections to geometry, topology, and string theory. Includes computations of Gromov-Witten and Donaldson-Thomas invariants.
Donaldson-Thomas and Gromov-Witten Theories - Part 9
Explore moduli spaces of algebraic curves and coherent sheaves, their invariants, and connections to geometry, topology, and string theory. Includes computations of Gromov-Witten and Donaldson-Thomas invariants.
Donaldson-Thomas and Gromov-Witten Theories - Part 8
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their connections to superstring theory.
Donaldson-Thomas and Gromov-Witten Theories - Part 7
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
Donaldson-Thomas and Gromov-Witten Theories - Part VI
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their connections to superstring theory.
Donaldson-Thomas and Gromov-Witten Theories - Part 5
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
Donaldson-Thomas and Gromov-Witten Theories - Part 4
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their applications in superstring theory.
Donaldson-Thomas and Gromov-Witten Theories - Part 3
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their applications in superstring theory.
Donaldson-Thomas and Gromov-Witten Theories - Part II
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their applications in superstring theory.
Donaldson-Thomas and Gromov-Witten Theories - Part I
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
Compactification of Moduli Spaces of Quantum Toric Stacks
Explores moduli spaces of quantum toric stacks and their compactification, extending toric varieties to stacky generalizations with finitely generated subgroups of R^d as "lattices".
The Horocycle Flow on the Moduli Space of Translation Surfaces
Explore the intricate dynamics of horocycle flows on translation surface moduli spaces, delving into mathematical concepts and their applications in geometry and dynamical systems.