## 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.

| Repeatable for credit

## MATH 284A: Geometry and Topology in Dimension 3

The Poincare conjecture and the uniformization of 3-manifolds. May be repeated for credit.

| Repeatable for credit

## MATH 284B: Geometry and Topology in Dimension 3

The Poincare conjecture and the uniformization of 3-manifolds. May be repeated for credit.

| Repeatable for credit

## MATH 285: Geometric Measure Theory

Hausdorff measures and dimensions, area and co-area formulas for Lipschitz maps, integral currents and flat chains, minimal surfaces and their singular sets.

| Repeatable for credit

Instructors:
Simon, L. (PI)

## MATH 286: Topics in Differential Geometry

May be repeated for credit.

| Repeatable for credit

Instructors:
Schoen, R. (PI)

## MATH 287: Introduction to optimal transportation

This will be an introductory course on Optimal Transportation theory. We will study Monge's problem, Kantorovich's problem, c-concave functions (also in the Riemannian setting), Wasserstein distance and geodesics (including a PDE formulation), applications to inequalities in convex analysis, as well as other topics, time permitting.

## 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.

| Repeatable for credit

## MATH 292A: Set Theory (PHIL 352A)

The basics of axiomatic set theory; the systems of Zermelo-Fraenkel and Bernays-Gödel. Topics: cardinal and ordinal numbers, the cumulative hierarchy and the role of the axiom of choice. Models of set theory, including the constructible sets and models constructed by the method of forcing. Consistency and independence results for the axiom of choice, the continuum hypothesis, and other unsettled mathematical and set-theoretical problems. Prerequisites: PHIL151 and
MATH 161, or equivalents.

## MATH 293A: Proof Theory (PHIL 353A)

Gentzen's natural deduction and sequential calculi for first-order propositional and predicate logics. Normalization and cut-elimination procedures. Relationships with computational lambda calculi and automated deduction. Prerequisites: 151, 152, and 161, or equivalents.

## MATH 295: Computation and Algorithms in Mathematics

Use of computer and algorithmic techniques in various areas of mathematics. Computational experiments. Topics may include polynomial manipulation, Groebner bases, computational geometry, and randomness. May be repeated for credit.

| Repeatable for credit

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