## 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 2016
| Repeatable for credit

## MATH 283: Topics in Algebraic and Geometric Topology

May be repeated for credit.

Terms: Spr
| Units: 3
| Repeatable for credit

Instructors:
Galatius, S. (PI)

## 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.

Last offered: Spring 2016
| Repeatable for credit

## MATH 284A: Geometry and Topology in Dimension 3

The Poincare conjecture and the uniformization of 3-manifolds. May be repeated for credit.

Last offered: Winter 2009
| Repeatable for credit

## MATH 284B: Geometry and Topology in Dimension 3

The Poincare conjecture and the uniformization of 3-manifolds. May be repeated for credit.

Last offered: Spring 2009
| Repeatable for credit

## MATH 286: Topics in Differential Geometry

May be repeated for credit.

Last offered: Spring 2016
| Repeatable for credit

## MATH 298: Graduate Practical Training

Only for mathematics graduate students. Students obtain employment in a relevant industrial or research activity to enhance their professional experience. Students submit a concise report detailing work activities, problems worked on, and key results. May be repeated for credit up to 3 units. Prerequisite: qualified offer of employment and consent of department. Prior approval by Math Department is required; you must contact the Math Department's Student Services staff for instructions before being granted permission to enroll.

Terms: Aut, Win, Spr, Sum
| Units: 1
| Repeatable for credit

Instructors:
Ryzhik, L. (PI)

## MATH 301: Advanced Topics in Convex Optimization (CME 375)

Modern developments in convex optimization: semidefinite programming; novel and efficient first-order algorithms for smooth and nonsmooth convex optimization. Emphasis on numerical methods suitable for large scale problems arising in science and engineering. Prerequisites: convex optimization (
EE 364), linear algebra (
Math 104), numerical linear algebra (
CME 302); background in probability, statistics, real analysis and numerical optimization.

Last offered: Winter 2015
| Repeatable for credit

## MATH 305: Applied mathematics through toys and magic

This course is a series of case-studies in doing applied mathematics on surprising phenomena we notice in daily life. Almost every class will show demos of these phenomena (toys and magic) and suggest open projects. The topics range over a great variety and cut across areas traditionally pigeonholed as physics, biology, engineering, computer science, mathematics ¿ but, instead of developing sophisticated mathematics on simple material, our aim is to extract simple mathematical understanding from sophisticated material which, at first, we may not yet know how to pigeonhole. In each class I will try to make the discussion self-contained and to give everybody something to take home, regardless of the background.

Last offered: Autumn 2015

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