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NTHRYS › PhD Assistance › Pure Mathematics

Pure Mathematics

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Pure Mathematics

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Algebraic Geometry and Moduli Spaces
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Arithmetic Geometry and Diophantine Equations
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Homotopy Theory and Higher Category Theory
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Derived Algebraic Geometry
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Noncommutative Geometry and Operator Algebras
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Symplectic Geometry and Hamiltonian Dynamics
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Differential Topology and Manifold Theory
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Representation Theory of Finite Groups
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Representation Theory of Lie Groups
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Quantum Groups and Hopf Algebras
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Homological Algebra and Cohomology Theories
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Algebraic Topology and Stable Homotopy
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K-Theory and Index Theory
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Knot Theory and Low-Dimensional Topology
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Gauge Theory and Yang-Mills Theory
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Floer Homology and Lagrangian Topology
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Geometric Representation Theory
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Lie Algebras and Enveloping Algebras
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Commutative Algebra and Scheme Theory
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Singularities and Resolution Techniques
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Intersection Theory and Chow Groups
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Number Theory and Elliptic Curves
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Algebraic Number Theory and Class Field Theory
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Analytic Number Theory and Zeta Functions
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Modular Forms and Automorphic Representations
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Galois Theory and Inverse Galois Problem
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Iwasawa Theory and p-adic Analysis
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Birational Geometry and Minimal Models
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Enumerative Geometry and Intersection Counts
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Toric Geometry and Fan Theory
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Derived Categories and Triangulated Categories
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Sheaf Cohomology and Characteristic Classes
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Hodge Theory and Kähler Geometry
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Categorical Logic and Topos Theory
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Category Theory and Natural Transformations
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Infinity Categories and Homotopy Limits
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Abstract Algebra and Group Theory
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Ring Theory and Noncommutative Rings
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Field Theory and Galois Extensions
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Combinatorial Algebra and Symbolic Computation
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Combinatorial Topology and Simplicial Complexes
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Graph Theory and Extremal Combinatorics
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Matroid Theory and Geometric Combinatorics
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Partition Functions and Combinatorial Species
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Real Algebraic Geometry and Positivity
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Tropical Geometry and Polyhedral Methods
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Logarithmic Structures and Log Geometry
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Toroidal Embeddings and Compactifications
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Stacks and Orbifold Geometry
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Deformation Theory and Obstruction Theory
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Perfectoid Spaces and Adic Geometry
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Chromatic Homotopy Theory and Morava K-theory
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Condensed Mathematics and Analytic Geometry
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Motivic Cohomology and Algebraic Cycles
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Derived Symplectic Geometry
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Microlocal Analysis and Sheaf Theory
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Prismatic Cohomology and p-adic Hodge Theory
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Khovanov Homology and Categorification
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Arithmetic Curves and Arithmetic Surfaces
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Fukaya Categories and Mirror Symmetry
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Equivariant Homotopy Theory and Group Actions
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Resurgent Transseries and Asymptotic Analysis
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Cluster Algebras and Quiver Representations
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Foliations and Foliated Bundles
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Higher Dimensional Algebraic Varieties
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Étale Cohomology and L-functions
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Instantons and Self-Dual Connections
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Spectral Sequences and Computational Topology
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Descent Theory and Faithfully Flat Descent
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Homotopy Type Theory and Univalent Foundations
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Stable Commutative Ring Spectra
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Orbifold Cohomology and Chen-Ruan Theory
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Schubert Calculus and Flag Varieties
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Exceptional Collections and Derived Equivalences
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Rational Homotopy Theory and Formality
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Heegner Points and Birch-Swinnerton-Dyer
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Convex Geometry and Polytopes
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Motivic Integration and Motivic Measures
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Étale Fundamental Groups and Galois Categories
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Configuration Spaces and Braid Groups
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Orbifold Fundamental Groups and Orbifold Covers
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Geometric Langlands Program and Automorphic Forms
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Stability Conditions on Triangulated Categories
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Quantum Invariants and Topological Quantum Field Theory
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Multiplicative Structure on Cohomology Rings
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Homomorphisms Between Symmetric Groups
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Asymptotic Invariants of Singularities
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Topological Data Analysis and Persistent Homology
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Universal Properties and Adjoint Functors
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Morse Theory and Critical Point Analysis
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Langlands Duality and Quantum Groups
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Arithmetic of Dynamical Systems
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Spin Geometry and Clifford Algebras
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Quantum Cohomology and Gromov-Witten Theory
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Nonstandard Analysis and Infinitesimals
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Affine Lie Algebras and Vertex Algebras
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Derived Functors and Extension Groups
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Holomorphic Dynamics and Julia Sets
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Slice Knots and Concordance
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Chromatic Homotopy Theory and Periodicity
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Derived Functors and Spectral Sequences
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Cyclic Cohomology and Noncommutative Analysis
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Rational Homotopy Theory and Formality
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Persistent Homology and Topological Data Analysis
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Mirror Symmetry and Homological Algebra
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Moment Maps and Geometric Invariant Theory
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Orbifold Cohomology and Chen-Ruan Theory
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Affine Hecke Algebras and Quantum Groups
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Étale Cohomology and l-adic Sheaves
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Intersection Cohomology and Perverse Sheaves
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Quantum Invariants and Three-Manifolds
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Heegaard Floer Homology and Contact Topology
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Instanton Homology and Knot Invariants
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Derived Noncommutative Algebraic Geometry
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Rational Points and Brauer-Manin Obstructions
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Arithmetic Intersections and Arakelov Theory
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Categorical Quantum Mechanics and Logic
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Fibered Categories and Stack Descent
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Stable Equivariant Homotopy Theory
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Motivic Spectral Sequences and Norm Maps
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Cohen-Macaulay Rings and Canonical Singularities
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Linkage and Liaison Theory in Algebra
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Tight Closure and Characteristic p Methods
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Homological Conjectures in Commutative Algebra
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Brane Transport and Categorical Invariants
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Microlocal Analysis and Constructible Sheaves
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Bordism and Cobordism Theories
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Loop Spaces and String Topology
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Donaldson Theory and Moduli of Connections
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Seiberg-Witten Theory and Monopole Equations
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Monopole Floer Homology and Instanton Theory
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Calabi-Yau Manifolds and Derived Categories
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Fano Varieties and Stability Theory
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Moduli of Curves and Gromov-Witten Theory
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Wall-Crossing and Stability Conditions
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Quiver Representations and Cluster Algebras
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Noncommutative Projective Geometry
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D-modules and Microlocalization
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Tensor Categories and Fusion Categories
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Vertex Algebras and Conformal Structures
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Kac-Moody Algebras and Invariant Theory
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Schubert Varieties and Parabolic Subgroups
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Torus Actions and GKM Theory
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Equivariant Localization and Fixed Point Formulas
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Hypergeometric Functions and Special Functions
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Lefschetz Hyperplane Theorem and Vanishing Theorems
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Abelian Varieties and Theta Functions
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Jacobian Varieties and Curve Geometry
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Chromatic Homotopy Theory and Morava Stabilizer Groups
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p-adic Hodge Theory and Galois Representations
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Equivariant Stable Homotopy and RO(G)-Grading
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Fano Varieties and Extremal Contractions
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Calabi-Yau Manifolds and Mirror Symmetry
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Elliptic Cohomology and Topological Modular Forms
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Cluster Algebras and Poisson Geometry
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Contact Topology and Legendrian Knots
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Motivic Integration and Nonsingular Varieties
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Spectral Sequences and Computational Homological Algebra
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Affine Hecke Algebras and Kazhdan-Lusztig Theory
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Braid Groups and Configuration Spaces
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Nonabelian Hodge Theory and Character Varieties
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Operads and Homotopy Algebras
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Knot Invariants and Quantum Algebra
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Hyperkähler Geometry and Twistor Theory
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Crystalline Cohomology and p-adic Differential Equations
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Donaldson-Thomas Theory and Wall-Crossing Formulas
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Arithmetic Statistics and L-function Families
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Tannaka Duality and Reconstruction Theorems
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Factorization Algebras and Quantum Field Theory
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Lattice Polytopes and Ehrhart Polynomials
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Symplectic Reduction and Moment Maps
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Stability Conditions and Bridgeland Stability
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Foliations and Characteristic Classes
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Moduli of Curves and Teichmüller Theory
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Rational Homotopy Theory and Formal Models
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Quantum Cohomology and Gromov-Witten Invariants
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Derived Algebraic Geometry over Simplicial Rings
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Heegaard Splittings and 3-Manifold Topology
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Canonical Metrics and Kähler-Einstein Equations
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Cyclotomic Fields and Iwasawa Main Conjecture
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Affine Flag Varieties and Zastava Spaces
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Tensor Categories and Braided Monoidal Structures
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Syzygies and Koszul Complexes
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Formal Schemes and Formal Algebraic Geometry
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Instanton Homology and Gauge Theory Invariants
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Lattice Models and Integrable Systems
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Abelian Varieties and Principally Polarized Moduli
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Moment-Angle Complexes and Polyhedral Products
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Perfectoid Spaces and Integral p-adic Geometry
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Vertex Algebras and Conformal Field Theory
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Chromatic Homotopy Theory and Chromatic Redshift
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Monsky-Washnitzer Cohomology and Rigid Geometry
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Motivic Homotopy Theory and A¹-Invariants
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Cluster Varieties and Poisson Structures
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Higher Algebra and Spectral Algebraic Geometry
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Motivic Measures and Arc Spaces
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Condensed Mathematics and Pyknotic Objects
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Higher Direct Images and Kodaira Vanishing
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Arithmetic Quantum Chaos and L-functions
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Anabelian Geometry and Grothendieck's Conjecture
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