• MATH 8250

    Partial Differential Equations
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    Last Taught

    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 8320

    Operator Theory I, II
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    Last Taught

    Fall 2025

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

  • MATH 8380

    Random Matrices
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    Last Taught

    Fall 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 8630

    Algebraic Number Theory
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    Last Taught

    Spring 2026

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

  • MATH 8850

    Topics in Algebraic Topology
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    Last Taught

    Fall 2026

    Selected advanced topics in algebraic topology.

  • MATH 8851

    Group Theory
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    Last Taught

    Spring 2026

    Studies the basic structure theory of groups, especially finite groups.

  • MATH 8998

    Non-Topical Research, Preparation for Research
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    Last Taught

    Fall 2026

    For master's research, taken before a thesis director has been selected.

  • MATH 8999

    Non-Topical Research
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    Last Taught

    Fall 2026

    For master's thesis, taken under the supervision of a thesis director.

  • MATH 9010

    Ramanujan-Serre Seminar
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    Last Taught

    Fall 2026

    Discusses topics from number theory.

  • MATH 9250

    Harmonic Analysis and PDEs
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    Last Taught

    Fall 2026

    Harmonic Analysis and PDEs seminar