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The standard branch of the matrix logarithm
Because of Euler’s identity , the complex exponential is not injective: for any complex and integer . As such, the complex logarithm is not well-defined as a single-valued function from to . However,...
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A remark on the lonely runner conjecture
The lonely runner conjecture is the following open problem: Conjecture 1 Suppose one has runners on the unit circle , all starting at the origin and moving at different speeds. Then for each runner,...
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Failure of the L^1 pointwise and maximal ergodic theorems for the free group
I’ve just uploaded to the arXiv my paper “Failure of the pointwise and maximal ergodic theorems for the free group“, submitted to Forum of Mathematics, Sigma. This paper concerns a variant of the...
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Cancellation for the multilinear Hilbert transform
I’ve just uploaded to the arXiv my paper “Cancellation for the multilinear Hilbert transform“, submitted to Collectanea Mathematica. This paper uses methods from additive combinatorics (and more...
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A differentiation identity
Here’s a cute identity I discovered by accident recently. Observe that and so one can conjecture that one has when is even, and when is odd. This is obvious in the even case since is a polynomial of...
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