MATH 272: Topics in Partial Differential Equations
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 273: Topics in Mathematical Physics (STATS 359)
Covers a list of topics in mathematical physics. The specific topics may vary from year to year, depending on the instructor's discretion. Background in graduate level probability theory and analysis is desirable.
Terms: not given this year, last offered Autumn 2018

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 275: Topics in Applied Mathematics: A World of Flows
The purpose of this course is to show beautiful surprises and instructive paradoxes in a maximal diversity of fluid phenomena, and to understand them with minimal models. Some deep currents will develop across multiple lectures. The prerequisites are fluency in the socalled `mathematical methods¿¿vector calculus, complex analysis, Fourier transform/series, ODEs, PDEs¿plus a willingness to wade into physics (classical more than quantum) at the advanced undergraduate level.
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 280: Evolution Equations in Differential Geometry
Terms: not given this year, last offered Winter 2014

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 282A: Low Dimensional Topology
The theory of surfaces and 3manifolds. Curves on surfaces, the classification of diffeomorphisms of surfaces, and Teichmuller space. The mapping class group and the braid group. Knot theory, including knot invariants. Decomposition of 3manifolds: triangulations, Heegaard splittings, Dehn surgery. Loop theorem, sphere theorem, incompressible surfaces. Geometric structures, particularly hyperbolic structures on surfaces and 3manifolds. May be repeated for credit up to 6 total units.
Terms: not given this year, last offered Autumn 2017

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 282B: Homotopy Theory
Homotopy groups, fibrations, spectral sequences, simplicial methods, DoldThom 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 for credit

Grading: Letter or Credit/No Credit
Instructors:
Ohrt, C. (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 Ktheory, including Bott periodicity, algebraic Ktheory, and indices of elliptic operators. Spectral sequences of AtiyahHirzebruch, Serre, and Adams. Cobordism theory, PontryaginThom theorem, calculation of unoriented and complex cobordism. May be repeated for credit up to 6 total units.
Terms: not given this year, last offered Spring 2018

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 283A: Topics in Topology
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 284: Topics in Geometric Topology
Incompressible surfaces, irreducible manifolds, prime decomposition, Morse theory, Heegaard diagrams, Heegaard splittings, the Thurston norm, sutured manifold theory, Heegaard Floer homology, sutured Floer homology.
Terms: not given this year, last offered Spring 2016

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 286: Topics in Differential Geometry
May be repeated for credit.
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
White, B. (PI)
Filter Results: