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NTHRYS › PhD Assistance › Topology Geometry

Topology Geometry

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Topology Geometry

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Persistent Homology and Topological Data Analysis
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Khovanov Homology and Quantum Invariants
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Symplectic Geometry and Hamiltonian Dynamics
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Floer Homology and Mirror Symmetry
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Geometric Measure Theory and Minimal Surfaces
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Kahler-Einstein Metrics and Extremal Geometry
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Derived Algebraic Geometry and Higher Stacks
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Topological Quantum Field Theory
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Gauge Theory and Yang-Mills Equations
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Instanton Floer Homology and 3-Manifolds
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Heegaard Floer Homology and Knot Theory
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Contact Geometry and Legendrian Knots
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Four-Manifold Topology and Donaldson Invariants
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Seiberg-Witten Theory and Smooth Invariants
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Calabi-Yau Manifolds and String Theory
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Riemannian Curvature and Positive Scalar Curvature
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Ricci Flow and Geometrization
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Kahler Geometry and Balanced Metrics
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Orbifold Geometry and Singularities
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Higher Category Theory and Topological Invariants
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Knot Concordance and 4-Genus
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Thurston Norm and Fibered Knots
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Homological Algebra and Derived Functors
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Cohomology Rings and Intersection Forms
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Characteristic Classes and Vector Bundles
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Cobordism Theory and Adams Spectral Sequence
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Homotopy Type Theory and Univalent Foundations
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Algebraic Topology and Model Categories
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Stratified Spaces and Intersection Homology
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Manifold Learning and Topological Methods
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Affine Differential Geometry and Convex Bodies
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Discrete Differential Geometry and Polyhedral Surfaces
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Geometric Group Theory and Word Metrics
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CAT(0) Spaces and Hyperbolic Geometry
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Right-Angled Artin Groups and Raags
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Teichmuller Theory and Moduli Spaces
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Kleinian Groups and 3-Dimensional Hyperbolic Geometry
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Conformal Geometry and Mobius Transformations
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Metric Geometry and Optimal Transport
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Riemannian Submersions and Fiber Bundles
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Spin Geometry and Dirac Operators
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Index Theory and Heat Kernels
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Orbifold Cohomology and Chen-Ruan Theory
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Gromov-Witten Invariants and Enumerative Geometry
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Quantum Cohomology and Small Quantum Rings
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Fukaya Categories and Homological Mirror Symmetry
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Knot Homologies and Categorification
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Sutured Manifold Theory and Bordered Homology
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Monopole Floer Homology and Link Invariants
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Knot Genus and Surfaces in 4-Space
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Topological Complexity and Motion Planning
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Floer Homology for Legendrian Submanifolds
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Quasigeodesic Stability and Hyperbolic Groups
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Knot Floer Homology and Surgery Formulas
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Instanton Moduli Spaces and Representation Varieties
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Tropical Geometry and Amoebas
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Geodesic Laminations and Foliations
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Hochschild Homology and Cyclic Structures
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Moduli of Algebraic Curves and Stacks
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Mapping Class Groups and Surface Bundles
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Anosov Diffeomorphisms and Dynamical Systems
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Moment Maps and Symplectic Reduction
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Thurston Geometries and Geometric Structures
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Derived Intersection Theory and Excess Intersections
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Lens Spaces and Surgery Invariants
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Heegaard Splittings and Thin Position
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Symplectic Fillings and Contact Boundaries
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Quantum Representations and Jones Polynomial
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Stable Concordance and Link Homologies
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Orbibundle Structures and Singular Fibrations
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Weinstein Manifolds and Exact Symplectic Geometry
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Plane Partitions and Toric Geometry
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Manifold Rigidity and Borel Conjecture
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Persistence Modules and Algebraic Stability
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Branched Coverings and Riemann Surfaces
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Geometric Deformation Theory and Milnor Fibers
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Turaev-Viro and State Sum Invariants
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Holomorphic Disks and Pseudoholomorphic Curves
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Sutured Instanton Homology and Tangles
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Fibered Links and Seifert Surfaces
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Resolution of Singularities and Blow-ups
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Automorphism Groups and Nielsen Realization
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Contact Homology and Legendrian Invariants
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Casson Handles and Four-Dimensional Topology
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Dehn Surgery and Three-Manifold Invariants
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Spherical Double Covers and Branched Covers
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Controlled Topology and Assembly Maps
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Toric Varieties and Polytope Combinatorics
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Lattice Homology and Q-Homology Planes
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Wrapped Fukaya Categories and Stops
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Seifert Fibered Spaces and Orbifold Singularities
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L-Spaces and Non-Thurston Structures
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Cylindrical Manifolds and Weinstein Structures
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Reshetikhin-Turaev Functors and TQFT
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Concordance Homomorphisms and Kernels
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Thurston Obstructions and Rational Maps
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Knotted Surfaces in Four-Dimensional Space
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Spectral Sequences and Page Computations
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Factorization Homology and Chiral Algebras
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Knot Genus and Optimal Surfaces
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Symplectic Capacities and Embedding Problems
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Lagrangian Cobordism and Exact Sequences
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Cluster Algebras and Positivity Phenomena
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Toric Geometry and Moment Polytopes
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Holomorphic Discs and Boundary Value Problems
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Geometric Quantization and Prequantum Bundles
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Equivariant Cohomology and GKM Theory
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Microlocal Sheaf Theory and Wrapped Sheaves
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Weinstein Structures and Liouville Manifolds
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Symplectic Resolutions and Crepant Categories
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Geometric Invariant Theory and Quotient Singularities
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Nonnegative Sectional Curvature and Soul Theory
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Controlled Topology and Surgery Theory
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Hochschild Homology and Derived Stacks
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Holomorphic Curves in Almost Complex Manifolds
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Filtrations in Heegaard Floer Theory
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Khovanov-Rozansky Homology and Higher Representation Theory
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Symplectic Field Theory and Pseudoholomorphic Foliations
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Instantons and Gauge Theory on 4-Manifolds
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Orbifold Singularities and Resolution Types
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Hofer Geometry and Bi-invariant Metrics
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Thurston-Bennequin Invariant and Contact Topology
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Morse Theory on Infinite-Dimensional Spaces
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Polyhedral Geometry and Polytope Algebra
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Exotic Smooth Structures on 4-Manifolds
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Aspherical Manifolds and Group Cohomology
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Nakajima Quiver Varieties and Symplectic Resolutions
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Legendrian Contact Homology and Augmentations
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Positive Loop Spaces and Totally Positive Matrices
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Cyclic Polytopes and Neighborliness
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Hyperplane Arrangements and Matroid Geometry
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Symplectic Groupoids and Poisson Structures
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Knot Invariants from Skein Relations
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Orbifold Bordism and Twisted Spin Structures
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Instanton Moduli and Representation Varieties
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Symplectic Toric Varieties and Delzant Polytopes
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Graded Modules and Topological Hochschild Homology
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Wrapping and Non-Exact Symplectic Manifolds
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Matroid Realization and Oriented Matroids
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Bott Periodicity and K-Theory Computations
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Moment-Angle Complexes and Torus Actions
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Symplectic Spinors and Quantization
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Mapping Class Groups and Torelli Groups
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Gromov-Hausdorff Convergence and Metric Limits
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Morse-Floer Theory for Symplectic Quotients
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Legendrian Fronts and Caustics
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Stiefel-Whitney Classes and Vector Bundle Obstruction
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Symplectic Fillings and Tight Contact Structures
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Foliations and Godbillon-Vey Invariant
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Convexity in Symplectic Geometry and Maximally Graded Spaces
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Symplectic Four-Manifolds and Elliptic Fibrations
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Equivariant Cohomology and Torus Actions
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Legendrian Weaves and Cluster Algebras
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Instantons and Knot Invariants
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Tropical Geometry and Curve Counts
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Alexandrov Spaces and Curvature Bounds
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Holomorphic Curves and Pseudoholomorphic Techniques
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Thurston Polytopes and Veering Triangulations
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Hyperplane Arrangements and Formality
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Braid Groups and Configuration Spaces
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Symplectic Capacities and Rigidity
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Monopole Equations and Three-Manifold Invariants
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Cluster Structures and Positivity Geometry
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Legendrian Surfaces and Exact Sequences
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Weinstein Structures and Liouville Domains
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Bridgeland Stability and Wall-Crossing
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Hyperbolic Volume and Simplicial Complexes
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Quasiconformal Maps and Teichmuller Space
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Symplectic Toric Geometry and Delzant Theory
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Categorical Resolutions and Tilting Theory
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Branched Coverings and Orbifold Invariants
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Wrapped Microlocal Theory and Sheaves
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Lagrangian Correspondences and Functors
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Simplicial Commutative Algebra and Derived Schemes
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Thurston Geometries and Orbifold Fibrations
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Pseudoholomorphic Discs and Weak Fillings
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Polygon Spaces and Inverse Kinematics
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Holonomy and Special Riemannian Geometry
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Symplectic Homology and Conical Singularities
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Knot Floer Homology and Concordance
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Foliations and Transverse Geometry
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Homological Mirror Symmetry and Noncommutative Geometry
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Asymptotic Expansion and Eta Invariants
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Quiver Varieties and Geometric Representation Theory
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Enumerative Invariants and Counting Curves
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Geodesic Flows and Dynamical Systems
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Character Varieties and Representation Spaces
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Submanifold Geometry and Normal Bundles
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Bordered Floer Homology and Pairing Theorems
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Fibered Links and Open Book Decompositions
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Knot Genus and Seifert Surfaces
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Categorical Morse Theory and Conormal Sheaves
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Orbifold Singularities and Resolution Invariants
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Lens Spaces and Surgery Diagrams
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Spin Structures and Dirac Spectra
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Immersions and Immersion Theory
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Geometric Flows and Parabolic PDEs
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Equivariant Cohomology and Moment Graph Algebras
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Legendrian Surfaces and Augmentation Categories
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Algebraic Cycles and Chow Groups
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