The Ph.D. in Mathematics at Princeton University emphasizes rigorous research and theoretical innovation across all major branches of mathematics. Below are dissertation topics covering algebraic, geometric, topological, and applied domains.
Geometric Langlands Program and Categorification Techniques
p-adic Hodge Theory and Arithmetic Geometry Applications
Ricci Flow and Its Role in Geometric Topology
Computational Approaches to Knot Invariants
Moduli Spaces in Algebraic Geometry and Mathematical Physics
Model Theory and O-Minimal Structures in Real Geometry
Analytic Number Theory and Distribution of Primes
Mirror Symmetry in Calabi–Yau Manifolds
Ergodic Theory and Measure Rigidity in Dynamical Systems
Noncommutative Geometry and Quantum Field Theory
Combinatorics in Matroid Theory and Optimization
Partial Differential Equations in Fluid Mechanics Modeling
Homotopy Theory and Higher Category Structures
Diophantine Equations in Arithmetic Dynamics
Spectral Graph Theory and Applications in Data Science
Algebraic K-Theory in Topological Contexts
Stochastic Processes and Brownian Motion in Complex Systems
Elliptic Curves and Rational Points in Cryptographic Contexts
Functional Analysis in Infinite Dimensional Spaces
Mathematical Foundations of Machine Learning Algorithms
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