## 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
5 times
(up to 15 units total)

Instructors:
Conrad, B. (PI)
;
Booher, J. (TA)

## MATH 215A: Complex Analysis, Geometry, and Topology

Analytic functions, complex integration, Cauchy's theorem, residue theorem, argument principle, conformal mappings, Riemann mapping theorem, Picard's theorem, elliptic functions, analytic continuation and Riemann surfaces.

Terms: Aut
| Units: 3

Instructors:
Medina Mardones, A. (PI)
;
Zhu, B. (TA)

## MATH 215B: Complex Analysis, Geometry, and Topology

Topics: fundamental group and covering spaces, homology, cohomology, products, basic homotopy theory, and applications. Prerequisites: 113, 120, and 171, or equivalent; 215A is not a prerequisite for 215B.

Terms: Win
| Units: 3

Instructors:
Cohen, R. (PI)
;
Alvarez-Gavela, D. (TA)

## MATH 215C: Complex Analysis, Geometry, and Topology

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.

Terms: Spr
| Units: 3

Instructors:
Maximo, D. (PI)
;
Ungemach, W. (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.

Terms: Aut
| Units: 3
| Repeatable
for credit

Instructors:
Vakil, R. (PI)
;
Zhou, Y. (TA)

## MATH 216B: Introduction to Algebraic Geometry

Continuation of 216A. May be repeated for credit.

Terms: Win
| Units: 3
| Repeatable
for credit

Instructors:
Vakil, R. (PI)
;
Tripathy, A. (TA)

## MATH 216C: Introduction to Algebraic Geometry

Continuation of 216B. May be repeated for credit.

Terms: Spr
| Units: 3
| Repeatable
for credit

Instructors:
Vakil, R. (PI)
;
Pan, D. (TA)

## 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
2 times
(up to 6 units total)

## 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: foundation in multivariable calculus and ordinary differential equations.

Terms: Aut
| Units: 3

Instructors:
Vasy, A. (PI)
;
Sing Long Collao, C. (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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