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.
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.
D-Modules and Toric Schobers
Exploring mirror symmetry using perverse sheaves of categories and schobers, with focus on B-side category in toric homological mirror symmetry and associated D-module characteristic cycles.
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.
Homotopy Path Algebras
Explore Homotopy Path Algebras and their applications in algebraic topology, sheaf theory, and toric geometry. Discover connections to homological mirror symmetry and recent developments in the field.
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.
Metric Reconstruction via Optimal Transport
Explores metric reconstruction using optimal transport theory, introducing Vietoris-Rips thickening to recover metric information from point samples in metric spaces, with applications to Riemannian manifolds.
Don Sheehy - Sensors, Sampling, and Scale Selection: A Homological Approach
Explore sensor networks, sampling techniques, and scale selection through algebraic topology. Learn innovative approaches to data analysis and geometric inference in complex systems.
The Geometry of Synchronization Problems and Learning Group Act
Geometric framework for synchronization problems using fibre bundles, twisted cohomology, and Hodge theory. Applications to learning group actions and subgroups from noisy data.
Stratified Covering Maps and Interleavings
Explore stratified covering maps and interleavings in algebraic topology, examining their applications and theoretical foundations.
Vin de Silva - Functors and Cosheaves for Topological Persistence
Explore functors and cosheaves in topological persistence, delving into advanced concepts of applied algebraic topology and their applications in data analysis.
Amit Patel - Generalized Persistence Diagrams
Explore generalized persistence diagrams in algebraic topology, examining their applications and theoretical foundations for advanced data analysis and topological insights.
Tropical Coordinates on the Space of Persistence Barcodes
Explore tropical coordinates in persistence barcodes, a key concept in applied algebraic topology, and their applications in data analysis and shape recognition.
Chad Giusti - Topology and Neural Computation
Explore the intersection of topology and neural computation, examining how mathematical concepts can enhance our understanding of brain function and artificial intelligence.