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91 - 100 of 165 results for: MATH

MATH 257C: Symplectic Geometry and Topology

Continuation of 257B. May be repeated for credit.
Terms: Spr | Units: 3
Instructors: Lin, Y. (PI)

MATH 258: Topics in Geometric Analysis

May be repeated for credit.
Terms: Win, Spr | Units: 3 | Repeatable for credit

MATH 263A: Infinite-dimensional Lie Algebras

Basics of Kac-Moody Lie algebras, which include both finite dimensional semisimple Lie algebras and their infinite-dimensional analogs, up to the Kac-Weyl character formula and Macdonald identities, and the Boson-Fermion correspondence. May be repeated for credit. Prerequisite: 210 or equivalent.
Last offered: Winter 2014 | Repeatable for credit

MATH 263B: Modular Representation Theory

Modular representation theory, a field largely created by Brauer, is the representation theory of finite groups over a field of characteristic p. It was a key tool in the classification of finite simple groups. Key features are the important roles played by projective modules, and the subtle relationship with the characteristic zero theory. Modular representation theory has strong similarities to the theory of groups of Lie type, with normalizers of p-subgroups playing the role of parabolics. Brauer and Green found deep relationships between the modular representation theory of the group and the simpler representation theory of such subgroups. In addition to such classical topics, we will look at some more recent developments.
Terms: Win | Units: 3 | Repeatable for credit
Instructors: Bump, D. (PI)

MATH 263C: Topics in Representation Theory

Terms: Spr | Units: 3 | Repeatable for credit

MATH 269: Topics in symplectic geometry

May be repeated for credit.
Terms: Win | Units: 3 | Repeatable for credit

MATH 272: Topics in Partial Differential Equations

Terms: Win | Units: 3 | Repeatable for credit
Instructors: Ryzhik, L. (PI)

MATH 282B: Homotopy Theory

Homotopy groups, fibrations, spectral sequences, simplicial methods, Dold-Thom theorem, models for loop spaces, homotopy limits and colimits, stable homotopy theory. May be repeated for credit up to 6 total units.
Terms: Win | Units: 3 | Repeatable 2 times (up to 6 units total)
Instructors: Galatius, S. (PI)

MATH 282C: Fiber Bundles and Cobordism

Possible topics: principal bundles, vector bundles, classifying spaces. Connections on bundles, curvature. Topology of gauge groups and gauge equivalence classes of connections. Characteristic classes and K-theory, including Bott periodicity, algebraic K-theory, and indices of elliptic operators. Spectral sequences of Atiyah-Hirzebruch, Serre, and Adams. Cobordism theory, Pontryagin-Thom theorem, calculation of unoriented and complex cobordism. May be repeated for credit up to 6 total units.
Terms: Spr | Units: 3 | Repeatable 2 times (up to 6 units total)

MATH 285: Geometric Measure Theory

Hausdorff measures and dimensions, area and co-area formulas for Lipschitz maps, integral currents and flat chains, minimal surfaces and their singular sets.
Terms: Aut | Units: 3 | Repeatable for credit
Instructors: Simon, L. (PI)
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