The aftermath of Bell's tablet PC lectures

These are snapshots of the scribbled over remains of
what appears on the projector at the end of class when
the lecture is on a tablet PC.

• Lecture 1 The improved Cauchy integral formula
• Lecture 2 Solving the "dee bar" problem and a lemma
• Lecture 3 Proof of the lemma
• Lecture 5 Solving the dee-bar problem in the plane, disc, and SCV
• Lecture 6 Applications to the Mittag-Leffler and Weierstrass theorems
• Lecture 7 Boundary behavior of the Cauchy transform
• Lecture 8 Hardy space, the Kerzman-Stein operator, the Plemelj formula
• Lecture 9 The Kerzman-Stein operator is smoothing, the Szegö projection
• Lecture 10 Orthogonal decomposition and the Szegö kernel
• Lecture 11 The Garabedian kernel, the Riemann map
• Lecture 12 Solving the Dirichlet problem using the Szegö projection
• Lecture 13 The Bergman space and kernel
• Lecture 14 Density lemmas for the Bergman space, Weyl's lemma
• Lecture 15 Transformation formula for Bergman kernels
• Lecture 16 Applications, quadrature domains
• Lecture 17 Domains with holes
• Lecture 18 The case of real analytic boundary
• Lecture 19 The Schwarz function
• Lecture 20 Simply connected quadrature domains
• Lecture 21 Transformation formula for the Szegö
• Lecture 22 Area quadrature domains, arc-length quadrature domains, and double quadrature domains
• Lecture 23 Proof of the Isoperimetric inequality!
• Lecture 24 More about quadrature domains
• Lecture 25 Dirichlet problem with rational data, Khavinson-Shapiro conjecture
• Lecture 26 Classical Neumann problem for the Laplacian
• Lecture 27 The double of a domain and the Schwarz function
• Lecture 28 Green's function and the Bergman kernel
• Lecture 29 The complementary kernel to the Bergman kernel
• Lecture 30 Harnack's inequality, the Hopf lemma, and conformal mapping
• Lecture 31 Smooth boundary behavior of biholomorphic mappings in SCV
• Lecture 32 Sketch of the proof, cont'd
• Lecture 33 The Ahlfors map and a generalized argument principle
• Lecture 34 Zeroes of the Ahlfors map
• Lecture 35 More about the Ahlfors map
• Lecture 36 Proper holomorphic mappings, transformation formulas
• Lecture 37 Zeroes of the Szegö kernel
• Lecture 39 More about domains with holes, harmonic measure functions
• Lecture 40 The matrix of periods
• Lecture 41 Dual of the space of holomorphic functions smooth up to the boundary
• Lecture 42 Dirichlet problem on double quadrature domains
• Lecture 43 Mapping problems in several complex variables

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