## MATH 263C: Topics in Representation Theory

May be repeated for credit.

Terms: Spr
| Units: 3
| Repeatable for credit

Instructors:
Bump, D. (PI)

## 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.

Terms: Win
| Units: 3

Instructors:
Eliashberg, Y. (PI)

## MATH 272: Topics in Partial Differential Equations

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Galkowski, J. (PI)

## 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: Spr
| Units: 3
| Repeatable for credit

Instructors:
Perlmutter, N. (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:
Galatius, S. (PI)

## 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 355: Graduate Teaching Seminar

Required of and limited to first-year Mathematics graduate students.

Terms: Spr
| Units: 1

Instructors:
Lucianovic, M. (PI)
;
White, B. (PI)

## MATH 360: Advanced Reading and Research

Terms: Aut, Win, Spr, Sum
| Units: 1-10
| Repeatable for credit

Instructors:
Bump, D. (PI)
;
Candes, E. (PI)
;
Carlsson, G. (PI)
...
more instructors for MATH 360 »

Instructors:
Bump, D. (PI)
;
Candes, E. (PI)
;
Carlsson, G. (PI)
;
Chatterjee, S. (PI)
;
Church, T. (PI)
;
Cohen, R. (PI)
;
Conrad, B. (PI)
;
Dembo, A. (PI)
;
Diaconis, P. (PI)
;
Eliashberg, Y. (PI)
;
Fox, J. (PI)
;
Galatius, S. (PI)
;
Ionel, E. (PI)
;
Kerckhoff, S. (PI)
;
Li, J. (PI)
;
Luk, J. (PI)
;
Mazzeo, R. (PI)
;
Papanicolaou, G. (PI)
;
Poulson, J. (PI)
;
Ryzhik, L. (PI)
;
Schoen, R. (PI)
;
Soundararajan, K. (PI)
;
Vakil, R. (PI)
;
Vasy, A. (PI)
;
Venkatesh, A. (PI)
;
Vondrak, J. (PI)
;
White, B. (PI)
;
Wright, A. (PI)
;
Ying, L. (PI)