Mirror Structure Constants via Non-Archimedean Analytic Disks
Exploration of mirror structure constants for smooth affine log Calabi-Yau varieties using non-archimedean analytic disks, generalizing previous constructions and discussing potential further applications.
Quivers, Curve Counting, and Fermionic Sums in Topology
Explore connections between quantum groups, vertex algebras, and quiver representations in topology. Discover how fermionic forms link these areas, shedding new light on enumerative geometry and curve counting.
Andras Nemethi- Multivariable Poincaré Series of Complex Singularities
Explore multivariable Poincaré series in complex singularities with Andras Nemethi. Delve into advanced mathematical concepts at the intersection of geometry, topology, and singularity theory.
Braid Monodromy and Divisibility of Alexander Polynomials of Real Singular Curves
Explores Alexander polynomials in algebraic geometry, focusing on braid monodromy symmetries of real plane curves and their impact on divisibility relations for Alexander invariants.
Decomposition of Definable Sets in Algebraically Closed Fields
Explore definable set decomposition in algebraically closed fields. Delve into geometric and topological aspects of group actions, connecting algebraic topology, geometry, and mathematical physics.
Deformation Theory for Finite Cluster Complexes
Explore geometric relationships between cluster varieties and complexes, focusing on finite cluster types with universal coefficients and their connection to Hilbert schemes via torus actions.
Pontrjagin Duality on Multiplicative Gerbes
Exploration of Pontrjagin Duality on Multiplicative Gerbes, proposing a generalization of the Twisted Drinfeld Double to continuous groups. Part of a conference on geometry, topology, group actions, and singularities.
Danny Ruberman- Diffeomorphism Groups of 4-Manifolds
Exploring unique 4-dimensional phenomena: infinite families of homeomorphic but non-diffeomorphic manifolds, and exotic behavior in diffeomorphism and homeomorphism groups.
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.
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.
Fake Projective Planes: Properties and Recent Progress
Explore fake projective planes: complex surfaces with unique properties, their construction via uniformization, and recent advancements in understanding their algebraic and geometric characteristics.
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.
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.
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.
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.
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.
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.
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 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.