MATH 263B: Quantum Groups and the Yang-Baxter Equation
Two classes of phenomena in mathematical physics, namely the solvable lattice models in statistical physics and Heisenberg spin chains lead to the same identity, namely the Yang-Baxter equation. Quasitriangular Hopf algebras (quantum groups), "braided monoidal category," such as Kuperberg's proof of the alternating sign conjecture, deformations of the Weyl character formula, and knot invariants such as the Jones polynomial. May be repeated for credit.
Terms: Spr
| Units: 3
| Repeatable
for credit
Instructors:
Bump, D. (PI)
MATH 269: Topics in symplectic geometry
May be repeated for credit.
Terms: Spr
| Units: 3
| Repeatable
for credit
Instructors:
Eliashberg, Y. (PI)
MATH 280: Evolution Equations in Differential Geometry
Terms: Aut, Win
| Units: 3
| Repeatable
for credit
Instructors:
Bamler, R. (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: Spr
| Units: 3
| Repeatable
2 times
(up to 6 units total)
Instructors:
Mirzakhani, M. (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: Win
| Units: 3
| Repeatable
2 times
(up to 6 units total)
Instructors:
Galatius, S. (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
2 times
(up to 6 units total)
Instructors:
Carlsson, G. (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.
Terms: Win
| Units: 3
| Repeatable
for credit
Instructors:
Kerckhoff, S. (PI)
MATH 286: Topics in Differential Geometry
May be repeated for credit.
Terms: Win, Spr
| Units: 3
| Repeatable
for credit
Instructors:
Brendle, S. (PI)
;
Schoen, R. (PI)
MATH 290B: Model Theory B (PHIL 350B)
Decidable theories. Model-theoretic background. Dense linear orders, arithmetic of addition, real closed and algebraically closed fields, o-minimal theories.
Terms: Aut
| Units: 1-3
| Repeatable
for credit
Instructors:
Mints, G. (PI)
MATH 310: Top Ten Algorithms of the 20th Century (CME 329)
A high-level survey course covering one algorithm per week: metropolis, simplex method, conjugate gradient, QR, quicksort, fast fourier transform, maxcut, fast multipole method, integer relation detection, and convex/semi-definite programming.
Terms: Aut
| Units: 3
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