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NTHRYS › PhD Assistance › Algebraic Geometry

Algebraic Geometry

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Algebraic Geometry

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Derived Categories and Homological Mirror Symmetry
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Moduli Spaces of Stable Curves
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Intersection Theory and Chow Rings
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Birational Geometry and Minimal Models
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Toric Varieties and Polytope Combinatorics
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Abelian Varieties and Principally Polarized Spaces
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Hodge Theory and Period Domains
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Calabi-Yau Manifolds and String Theory
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Enumerative Geometry and Gromov-Witten Invariants
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Singularities and Resolution Techniques
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Sheaf Cohomology and Vanishing Theorems
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Algebraic K-Theory and Motivic Cohomology
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Derived Algebraic Geometry and Stacks
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Rational Points on Varieties
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Arithmetic Surfaces and Arakelov Geometry
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Fano Varieties and Del Pezzo Surfaces
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Algebraic Surfaces and Invariants
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Vector Bundles on Curves and Moduli
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Quantum Cohomology and Symplectic Geometry
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Grothendieck Duality and Serre Duality
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Secant Varieties and Tensor Decomposition
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Symbolic Powers and Integral Closure
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Bezout Theory and Intersection Multiplicities
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K3 Surfaces and Automorphisms
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Stability Conditions and Wall Crossing
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Tropical Geometry and Piecewise Linear Structures
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Invariant Theory and Quotient Varieties
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Representation Varieties and Character Schemes
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Affine and Projective Schemes
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Neron Models and Arithmetic Geometry
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Cremona Transformations and Birational Maps
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Cohen-Macaulay Varieties and Canonical Modules
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Hilbert Schemes and Parameter Spaces
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Syzygies and Castelnuovo-Mumford Regularity
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Amplfication and Numerical Geometry
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Goppa Codes and Algebraic Geometry Codes
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Pfaffian Varieties and Determinantal Equations
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Graded Rings and Projective Embeddings
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Fontaine-Laffaille Modules and p-Adic Geometry
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Supersingular Varieties in Characteristic p
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Secant Lines and Classical Enumerative Problems
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Orbifold Cohomology and Chen-Ruan Theory
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Vanishing Ideals and Combinatorial Commutative Algebra
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Categorical Resolutions and Noncommutative Geometry
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Tropical Varieties and Log Structures
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Berkovich Spaces and Non-Archimedean Geometry
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Valuations and Singularity Exponents
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Cluster Algebras and Positivity
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Monodromy and Galois Groups of Covers
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Perfect Ideals and Resolutions
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Derived Stacks and Higher Categorical Methods
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Motive Theory and Motivic Integration
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Bridgeland Stability and D-Brane Categories
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Logarithmic Geometry and Log-Smooth Degenerations
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Derived Invariants and Categorical Invariants
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Positivity and Valuative Methods
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Singularities in Positive Characteristic Geometry
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Derived Representation Schemes and Stacks
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Categorical Resolutions and Noncommutative Deformations
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Frobenius Morphisms and Arithmetic Schemes
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Moduli of Holomorphic Differential Forms
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Refined Gromov-Witten Invariants and Quantum Cohomology
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Spaces of Rational Curves and Unirationality
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Sheaf Quantization and Microlocal Analysis
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Torus Equivariant Cohomology and Localization
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Homological Mirror Symmetry and Fukaya Categories
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Instanton Invariants and Moduli of Vector Bundles
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Bridgeland Stability on Surfaces and 3-Folds
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Perfectoid Spaces and Adic Geometry
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Multilinear Algebra and Tensor Rank Varieties
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Lattice Polytopes and Toric Degenerations
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K-Stability and Kahler-Einstein Metrics
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Periods of Algebraic Varieties and Hodge Conjecture
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Sato-Tate Distributions and L-Functions
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Categorical Structures on Derived Categories
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Geometric Langlands Program and D-Modules
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Reduction Modulo Prime and Specialization
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Cohomological Field Theories and Correlators
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Mixed Hodge Structures and Weight Filtrations
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Étale Cohomology and Galois Representations
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Elliptic Surfaces and Fibrations
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Stability and Destabilizing Sequences
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Canonical and Anticanonical Systems
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Deformation Theory and Obstruction Spaces
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Tautological Classes and Cycle Classes
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Bridgeland Stability for 3-Fold Flopping Contractions
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Motivic Nearby Cycles and Singularity Theory
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Cluster Algebras from Quivers and Geometry
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Intersection Cohomology and Perverse Sheaves
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Modular Forms and Arithmetic Surfaces
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Equivariant Derived Categories and Quotient Singularities
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Chow Groups of Zero-Cycles
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Brill-Noether Theory on Curves
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Spherical Double Affine Hecke Algebras
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Prym Varieties and Spectral Curves
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Convex Geometry of Weight Polytopes
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Hyperplane Arrangements and Cohomology
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Gromov-Witten Invariants of Orbifolds
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Universal Formulas and Localization Techniques
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Sheaf Extensions and Ext-Algebras
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Geometric Langlands Program and Automorphic Forms
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Higher Dimensional Fano Varieties Classification
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Derived Categories of Coherent Sheaves
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Moduli of Sheaves and Bridgeland Stability
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Rational Curves and Unirational Varieties
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Equivariant Intersection Theory and Localization
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Foliations on Algebraic Varieties
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Derived Stacks and Higher Categorical Structures
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Positivity Cones in Algebraic Varieties
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Manin-Mumford Conjecture and Unlikely Intersections
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Brill-Noether Theory on Singular Curves
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Logarithmic Schemes and Toroidal Geometry
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Frobenius Splitting and Tight Closure
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Perverse Sheaves and Intersection Cohomology
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Nested Hilbert Schemes and Quot Schemes
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Matrix Factorizations and Singularity Theory
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Seshadri Constants and Positivity of Line Bundles
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Exceptional Collections and Semiorthogonal Decompositions
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Stability of Vector Bundles and Moduli
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Jet Schemes and Arc Spaces
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Motivic Integration and Stringy Invariants
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Derived Equivalences and Non-Commutative Geometry
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Iwahori-Whittaker Functions and Affine Hecke Algebras
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Donaldson-Thomas Invariants and Counting
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Pandharipande-Thomas Stable Pairs Theory
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Mirror Symmetry for Fano Varieties
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Higher Genus Curves and Noether-Lefschetz Locus
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Derived Autoequivalences and Stability Conditions
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Non-Reduced Schemes and Scheme Structure
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Finite Morphisms and Galois Theory
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Étale Cohomology and L-Adic Sheaves
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Rigid Analytic Varieties and Formal Schemes
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Modular Curves and Shimura Varieties
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Gonality and Brill-Noether Divisors
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Splitting Type of Vector Bundles
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Cox Rings and Mori Dream Spaces
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Toric Embeddings and Moment Polytopes
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Theta Functions and Jacobian Varieties
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Intermediate Jacobians and Hodge Conjecture
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Kummer Surfaces and Hyper-Kahler Geometry
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Fano Threefolds and Mori Geometry
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Stable Maps and Virtual Moduli Classes
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Moduli of Hypersurfaces and Pathologies
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F-Singularities and Characteristic p Methods
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Multiplier Ideals and Singularity Invariants
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Étale Cohomology and Galois Actions
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Intersection Homology and Perverse Sheaves
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Deformation Theory and Obstruction Spaces
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Bridgeland Stability and D-brane Categories
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Grothendieck-Riemann-Roch Theorem Applications
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Moduli of Abelian Surfaces and Siegel Varieties
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Derived Autoequivalences and Stability
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Crystal Bases and Quantum Groups
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Generic Singularities and Whitney Stratification
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Brill-Noether Theory and Rank Conditions
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Positivity Cones and Effective Divisors
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Categorical Symplectic Reduction
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Monge-Ampère Equations and Kähler Geometry
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Langlands Duality and Spectral Geometry
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Virtual Fundamental Classes and GW Theory
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Minimal Generating Sets and Ideal Generators
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Stability of Bundles and Yang-Mills Equations
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Tautological Rings and Psi Classes
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Elliptic Fibrations and Picard Lattices
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O-Minimality and Semi-Algebraic Geometry
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Symplectic Quotient Singularities
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Gromov Compactness and Curve Moduli
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Donaldson Invariants and Gauge Theory
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Homotopy Sheaves and Higher Topos Theory
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Moment Maps and Symplectic Reduction
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Character Varieties and Representation Moduli
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Nakayama Categories and Recollements
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Intersection Algorithms and Computational Methods
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Invariant Differential Forms and Canonical Divisors
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Rational Curves and Pathologies
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Serre-Tate Theory and p-Adic Deformations
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Coherent Sheaves on Projective Spaces
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Bott Periodicity and K-Theory
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Instanton Moduli and Gauge Fixing
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Exceptional Collections and Stability Chains
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Jacobian Fibrations and Height Functions
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Quantum Corrections and Mirror Formulas
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Divisor Class Groups and Picard Schemes
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Holomorphic Curves and Floer Homology
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Weil Divisors and Cartier Divisors
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Tropical Intersection and Piecewise Linearity
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Poisson Structures and Noncommutative Resolution
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Spectral Sequences and Derived Functors
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Automorphism Groups and Dynamical Systems
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Reduced Schemes and Nilpotents
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Morse Theory on Manifolds with Corners
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Fundamental Groups and Etale Covers
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Derived Stacks and Higher Categorical Structures
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Graded Bialgebras and Hopf Modules
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Hilbert Functions and Graded Modules
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Mirror Symmetry and Categorical Enumerative Invariants
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Faltings Height and Arithmetic Intersection
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Singularities in Positive and Mixed Characteristic
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Non-Archimedean Geometry and Analytic Spaces
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Dg-Algebras and Noncommutative Resolutions
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