## MATH 210C: Lie Theory

Topics in Lie groups, Lie algebras, and/or representation theory. Prerequisite:
math 210B. May be repeated for credit.

Terms: Spr
| Units: 3
| Repeatable for credit

Instructors:
Bump, D. (PI)
;
Rosengarten, Z. (TA)

## MATH 215A: Algebraic Topology

Topics: fundamental group and covering spaces, basics of homotopy theory, homology and cohomology (simplicial, singular, cellular), products, introduction to topological manifolds, orientations, Poincare duality. Prerequisites: 113, 120, and 171.

Terms: Aut
| Units: 3

Instructors:
Carlsson, G. (PI)
;
De Groote, C. (TA)

## MATH 215B: Differential Topology

Topics: Basics of differentiable manifolds (tangent spaces, vector fields, tensor fields, differential forms), embeddings, tubular neighborhoods, integration and Stokes¿ Theorem, deRham cohomology, intersection theory via Poincare duality, Morse theory. Prerequisite: 215A

Terms: Win
| Units: 3

Instructors:
Perlmutter, N. (PI)
;
Reinhold, J. (TA)

## MATH 215C: Differential Geometry

This course will be an introduction to Riemannian Geometry. Topics will include the Levi-Civita connection, Riemann curvature tensor, Ricci and scalar curvature, geodesics, parallel transport, completeness, geodesics and Jacobi fields, and comparison techniques. Prerequisites 146 or 215B

Terms: Spr
| Units: 3

Instructors:
Mazzeo, R. (PI)
;
Ward, A. (TA)

## MATH 216A: Introduction to Algebraic Geometry

Algebraic curves, algebraic varieties, sheaves, cohomology, Riemann-Roch theorem. Classification of algebraic surfaces, moduli spaces, deformation theory and obstruction theory, the notion of schemes. May be repeated for credit. Prerequisites: 210ABC or equivalent.

Last offered: Autumn 2015
| Repeatable for credit

## MATH 216B: Introduction to Algebraic Geometry

Continuation of 216A. May be repeated for credit.

Last offered: Winter 2016
| Repeatable for credit

## MATH 216C: Introduction to Algebraic Geometry

Continuation of 216B. May be repeated for credit.

Last offered: Spring 2016
| Repeatable for credit

## MATH 217C: Complex Differential Geometry

Complex structures, almost complex manifolds and integrability, Hermitian and Kahler metrics, connections on complex vector bundles, Chern classes and Chern-Weil theory, Hodge and Dolbeault theory, vanishing theorems, Calabi-Yau manifolds, deformation theory.

Last offered: Winter 2015
| Repeatable for credit

## MATH 220: Partial Differential Equations of Applied Mathematics (CME 303)

First-order partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems. Prerequisite: Basic coursework in multivariable calculus and ordinary differential equations, and some prior experience with a proof-based treatment of the material as in
Math 171 or
Math 61CM (formerly
Math 51H).

Terms: Aut
| Units: 3

Instructors:
Ryzhik, L. (PI)
;
Liu, F. (TA)

## MATH 221A: Mathematical Methods of Imaging (CME 321A)

Image denoising and deblurring with optimization and partial differential equations methods. Imaging functionals based on total variation and l-1 minimization. Fast algorithms and their implementation.

Last offered: Winter 2014

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