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  • MATH 8250

    Partial Differential Equations
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    Fall 2025

    Theory of distributions. Sobolev spaces and their properties (trace and embedding theorems). Theory of elliptic equations. Time-dependent partial differential equations: parabolic and hyperbolic equations. Topics in nonlinear partial differential equations. Prerequisites: MATH 7410 and 7250.

  • MATH 8310

    Operator Theory I, II
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    Spring 2025

    Topics in the theory of operators on a Hilbert space and related areas of function theory.

  • MATH 8320

    Operator Theory I, II
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    Fall 2025

    Topics in the theory of operators on a Hilbert space and related areas of function theory.

  • MATH 8360

    Stochastic Calculus and Differential Equations
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    Spring 2025

    This course presents the basic theory of stochastic differential equations and provides examples of its applications. It is an essential topic for students preparing to do research in probability. Topics covered include a review of the relevant stochastic process and martingale theory; stochastic calculus including Ito's formula; existence and uniqueness for stochastic differential equations, strong Markov property; and applications. Prerequisite: MATH 7360 and 7370, or instructor permission.

  • MATH 8380

    Random Matrices
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    Spring 2026

    Discusses fundamental problems and results of the theory of random matrices, and their connections to tools of algebra and combinatorics: Wigner's semicircle law, free probability, Gaussian, circular, and beta ensembles of random matrices, bulk and edge asymptotics and universality, Dyson's Brownian motion, determinantal point processes, and discrete analogues of random matrix models. Prerequisite: MATH 7360 or instructor permission.

  • MATH 8620

    Algebraic Geometry
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    3.93

    Last Taught

    Spring 2025

    Studies the foundations of algebraic geometry.

  • MATH 8630

    Algebraic Number Theory
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    Spring 2026

    Theory of number fields and local fields, ramification theory, further topics as chosen by instructor.

  • MATH 8710

    Lie Algebras
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    3.82

    Last Taught

    Fall 2025

    Studies basic structure theory of Lie algebras.

  • MATH 8750

    Topology of Manifolds
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    3.99

    Last Taught

    Fall 2025

    Studies regular and critical values, gradient flow, handle decompositions, Morse theory, h-cobordism theorem, Dehn's lemma in dimension 3, and disk theorem in dimension 4. Prerequisite: Math 5770.

  • MATH 8850

    Topics in Algebraic Topology
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    Spring 2026

    Selected advanced topics in algebraic topology.