## MATH 263B: Crystal Bases: Representations and Combinatorics

Crystal Bases are combinatorial analogs of representation theorynof Lie groups. We will explore different aspects of thesenanalogies and develop rigorous purely combinatorial foundations.

Last offered: Winter 2016
| Repeatable for credit

## MATH 263C: Topics in Representation Theory

May be repeated for credit.

Last offered: Spring 2015
| Repeatable for credit

## 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.

Terms: Win
| Units: 3
| Repeatable for credit

Instructors:
Eliashberg, Y. (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.

Last offered: Winter 2013

## MATH 272: Topics in Partial Differential Equations

Terms: Spr
| 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.

Terms: Spr
| Units: 3

Instructors:
Chatterjee, S. (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: Win
| Units: 3
| Repeatable for credit

Instructors:
Wright, A. (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)

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