## 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 2017
| 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 2018

## MATH 272: Topics in Partial Differential Equations

NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.

Terms: Win
| Units: 3
| Repeatable
for credit

Instructors:
Ryzhik, L. (PI)

## 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.

Last offered: Autumn 2018
| Repeatable
for credit

## MATH 275: Topics in Applied Mathematics: A World of Flows II

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. The prerequisites are fluency in the so-called "mathematical methods", plus ability to think physics at the advanced undergraduate level. The content will be the same as that of winter 2019 (but different from that of winter 2020). nnNOTE: Undergraduates must obtain instructor permission and pass a test to enroll. Undergraduates interested in taking the course should contact the instructor no later than the first week of class, providing information about performance in prior coursework.

Terms: Aut
| Units: 3
| Repeatable
for credit

Instructors:
Tokieda, T. (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.

Last offered: Autumn 2017
| Repeatable
for credit

## 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.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.

Last offered: Winter 2020
| Repeatable
2 times
(up to 6 units total)

## 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.

Last offered: Spring 2018
| Repeatable
2 times
(up to 6 units total)

## MATH 283A: Topics in Topology

Topics of contemporary interest in topology. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.

Terms: Aut
| Units: 3
| Repeatable
for credit

Instructors:
Manolescu, C. (PI)

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