-
The Lovász Local Lemma
A proof of the Lovász local lemma, which states that if we have a collection of bad events with only a few 'local' dependencies, then we avoid all of them with positive probability.
-
Anticoncentration of Random Subset Sums
A proof of Erdős's theorem that random sums of the form $\varepsilon_1a_1 + \cdots + \varepsilon_na_n$ (for random $\varepsilon_i \in \{0, 1\}$ and fixed $a_i$) cannot be too concentrated.
-
Adjoint of a Compact Operator
A proof of the theorem from functional analysis that the adjoint of a compact linear operator between Banach spaces is also compact.
-
Perfect Power Polynomials
Which integer-coefficient polynomials only attain values which are perfect powers?
-
Tournament of Towns
Some cool problems from the Tournament of Towns.