printer friendly pageMATH 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
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 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
2 times
(up to 6 units total)
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
2 times
(up to 6 units total)
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
2 times
(up to 6 units total)
MATH 283A: Topics in Topology
Last offered: Winter 2018
| 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
3 times
(up to 3 units total)
Instructors:
Ryzhik, L. (PI)
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