## MATH 269: Topics in symplectic geometry

May be repeated for credit.

Last offered: Winter 2015
| Repeatable for credit

## MATH 270: Geometry and Topology of Complex Manifolds

Complex manifolds, Kahler manifolds, curvature, Hodge theory, Lefschetz theorem, Kahler-Einstein equation, Hermitian-Einstein equations, deformation of complex structures. May be repeated for credit.

Last offered: Winter 2008
| Repeatable for credit

## MATH 271: The H-Principle

The language of jets. Thom transversality theorem. Holonomic approximation theorem. Applications: immersion theory and its generaliazations. Differential relations and Gromov's h-principle for open manifolds. Applications to symplectic geometry. Microflexibility. Mappings with simple singularities and their applications. Method of convex integration. Nash-Kuiper C^1-isometric embedding theorem.

Last offered: Winter 2013

## MATH 272: Topics in Partial Differential Equations

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Ryzhik, L. (PI)

## MATH 280: Evolution Equations in Differential Geometry

Last offered: Winter 2014
| Repeatable for credit

## MATH 282A: Low Dimensional Topology

The theory of surfaces and 3-manifolds. 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 3-manifolds: triangulations, Heegaard splittings, Dehn surgery. Loop theorem, sphere theorem, incompressible surfaces. Geometric structures, particularly hyperbolic structures on surfaces and 3-manifolds. May be repeated for credit up to 6 total units.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Kerckhoff, S. (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 for credit

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 for credit

Instructors:
Medina Mardones, A. (PI)

## MATH 283: Topics in Algebraic and Geometric Topology

May be repeated for credit.

Terms: Spr
| Units: 3
| Repeatable for credit

Instructors:
Carlsson, G. (PI)

## MATH 283A: Topics in Topology

May be repeated for credit.

Last offered: Winter 2011

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