March 1st
Today I learned that local fields $F$ have character group $\widehat F$ isomorphic to themselves, from the MIT notes I've been reading. (continue reading...)
March 2021
March 2nd
Today I learned a proof of the classification of finitely generated abelian groups from the Smith normal form, from here . (continue reading...)
March 3rd
Today I learned (formally) about locally constant functions. (continue reading...)
March 4th
Today I learned some examples of $p$-adic geometry being horrible, from this undergraduate paper . (continue reading...)
March 5th
Today I learned about multiplicative (quasi)characters of local fields, from the MIT notes as usual. (continue reading...)
March 6th
Today I learned a little motivation for the compact-open topology: the evaluation map is continuous, from the nlab page . (continue reading...)
March 7th
Today I learned that determining if a single-variable (!) algebraic expression is identically $0$ is uncomputable. (continue reading...)
March 8th
Today I learned some more solid motivation for the compact-open topology, again from the nlab page . (continue reading...)
March 9th
Today I learned a way generating functions explicitly intersects with additive combinatorics. (continue reading...)
March 10th
Today I learned that the law of the excluded middle fails in homotopy type theory, from the Homotopy Type Theory book of course. (continue reading...)
March 11th
Today I learned a little about local $\zeta$-functions. (continue reading...)
March 12th
Today I learned the details of the proof of the local $\zeta$ functional equation. (continue reading...)
March 13th
Today I learned the definition of a sheaf. (continue reading...)
March 14th
Today I learned about one-point compactification, from the nlab page for example. (continue reading...)
March 15th
Today I learned how to fix the law of the excluded middle in homotopy type theory, from the homotopy type theory book as usual. (continue reading...)
March 16th
Today I learned about proposition truncation. (continue reading...)
March 17th
Today I learned about using lattice-attacks to solve the small inverse problem, directly from the Boneh and Durfee paper . (continue reading...)
March 18th
Today I learned a cute combinatorial proof from the AIME II. (continue reading...)
March 19th
Today I learned a different framing of the (weak) approximation theorem for $\AA_K.$ (continue reading...)
March 20th
Today I learned the proof that a number field $K$ is discrete and cocompact in its adele ring $\mathbb A_K.$ (continue reading...)
March 21st
Today I learned about univalence validating synthetic type construction. (continue reading...)
March 22nd
Today I learned about the axiom of choice in homotopy type theory. (continue reading...)
March 23rd
Today I learned a cute application of a generalized Eisenstein's criterion. (continue reading...)
March 24th
Today I learned the Zeckendorf decomposition of positive integers into nonconsecutive Fibonacci numbers. (continue reading...)
March 25th
Today I learned that the expected number of cycles in the cycle decomposition of a random permutation on $n$ letters is $H_n.$ (continue reading...)
March 26th
Today I learned a small extension of Euclidean proofs of Dirichlet's theorem, from this paper . (continue reading...)
March 27th
Today I learned the proof of the adelic poisson summation formula\todo{} (continue reading...)
March 28th
Today I learned the proof of the global zeta functional equation. (continue reading...)
March 29th
Today I learned some stuff around the pigeonhole principle. (continue reading...)
March 30th
Today I learned the proof that meromorphic functions are conformal (i.e., angle-perserving) almost everywhere. (continue reading...)
March 31st
Today I learned that the Zeckendorf decomposition from a few days ago in fact gives the least number of Fibonacci numbers a positive integer can be decomposed into by (possibly repeated) Fibonacci numbers. (continue reading...)