UC’s PhD in Mathematics offers deep training in algebra, analysis, geometry, and applied math, preparing scholars for academia, finance, and tech.
Homological study of persistent topology in complex networks
Spectral analysis of Schrödinger operators with quasi-periodic potentials
Finite-difference schemes proving stability of nonlinear wave equations
Elliptic-curve cryptography implementation benchmarking on IoT devices
Stochastic calculus model pricing weather derivatives under climate trends
Optimal transport approach to generative adversarial network training
Dynamics of coupled map lattices exhibiting chimera states
Category-theoretic framework linking type theory and quantum protocols
Markov-chain mixing time bounds for random walks on hypergraphs
Numerical solution of Monge–Ampère equations for reflector design
Variational principle derivation of mean-field games in economics
Interactive theorem-prover exploration of Langlands correspondences
Topological data analysis of climate-model ensemble outputs
Machine-assisted proof verification for combinatorial identities
Public lecture series on the Riemann Hypothesis and data security
Workshop mentoring high-school girls in advanced problem solving
White paper on ethics of automated proof verification systems
Graph-theory study of power-grid resilience under cascading failures
Quantum random-walk algorithms for search problems
Conference on interdisciplinary applications of discrete geometry
Delve into mathematical frontiers with UC’s theory-rich PhD.
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