## MATH 272: Topics in Partial Differential Equations

Terms: Spr
| Units: 3
| Repeatable for credit

Instructors:
Berestycki, H. (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: Aut
| Units: 3
| Repeatable for credit

Instructors:
Chatterjee, S. (PI)

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

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. Some deep currents will develop across multiple lectures. The prerequisites are fluency in the so-called `mathematical methods¿¿vector calculus, complex analysis, Fourier transform/series, ODEs, PDEs¿plus a willingness to wade into physics (classical more than quantum) at the advanced undergraduate level.

Terms: Win
| 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.

Terms: Win
| Units: 3
| Repeatable for credit

Instructors:
Ohrt, C. (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.

Last offered: Spring 2018
| Repeatable for credit

## MATH 283A: Topics in Topology

Last offered: Winter 2018
| Repeatable for credit

## 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 286: Topics in Differential Geometry

May be repeated for credit.

Last offered: Spring 2016
| Repeatable for credit

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