
Recent Posts
 Zeros of random polynomials
 Hopf fibration double covers circle bundle of sphere
 Euler’s formula e^ix = cos x + i sin x: a geometric approach
 An inequality for functions on the plane
 Weighted isoperimetric inequalities in warped product manifolds
 FaberKrahn inequality
 Why is a² + b² ≥ 2ab ?
 A remark on the divergence theorem
 The CauchySchwarz inequality and the Lagrange identity
 On the existence of a metric compatible with a given connection
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Category Archives: Complex analysis
Zeros of random polynomials
Given a polynomial , where the coefficients are random, what can we say about the distribution of the roots (on )? Of course, it would depend on what “random” means. Here, “random” means that the sequence is an i.i.d. sequence … Continue reading
Posted in Algebra, Complex analysis, Potential theory, Probability
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Euler’s formula e^ix = cos x + i sin x: a geometric approach
Today I mentioned the famous Euler’s formula briefly in my calculus class (when discussing hyperbolic functions, lecture notes here): where is a solution to (usually denoted by “”, but indeed there is no singlevalued square root for complex numbers, or … Continue reading
Posted in Analysis, Calculus, Complex analysis, Geometry
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Complex analysis – Problem solving strategies.
This post is written in spirit of Terrance Tao’s post on problem solving strategies in real analysis. Our emphasis will be on concrete techniques with plenty of examples (many are taken from past prelim questions in UW).
Posted in Complex analysis
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Principle of subordination
First we recall the statement of Schwarz’s lemma, which is a basic result in complex analysis. Let be the unit disk in . Schwarz’s lemma. Let . If for all and , then , and for all . If or … Continue reading
Posted in Complex analysis
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