UVA’s PhD in Mathematics cultivates independent scholars in abstract theory, mathematical logic, algebraic topology, differential geometry, and computational methods. The program supports students aiming for academic careers or high-level analytical roles in technology, finance, cryptography, or government research. Emphasis is placed on publication, conference presentation, and collaborative inquiry across disciplines such as physics, CS, and engineering.
Applications of sheaf theory in algebraic geometry
Homology theories in topological data analysis (TDA)
Advanced study of Ricci curvature in Riemannian manifolds
Langlands program: representation theory of p-adic groups
Spectral sequences in cohomology of fiber bundles
Formal logic systems and consistency theorems
Algebraic K-theory and applications in number theory
Automorphic forms and L-functions in analytic number theory
Dynamical systems and chaos in weather modeling
Tensor calculus applications in general relativity
Moduli spaces in mathematical physics
Descent theory in commutative algebra
Ergodic theory for statistical mechanics applications
Hodge theory in complex algebraic varieties
Infinite-dimensional Lie algebra classification problems
Push the boundaries of modern mathematics with UVA’s internationally connected PhD program.
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