# Category Uncategorized

## The dome and the egg

Il Cattedrale di Santa Maria del Fiore in Florence is a masterpiece church. I read a story in John Kay’s book Obliquity [1] about the history of the dome that I find worth sharing with you here in case you don’t already know it. Filippo Brunelleschi was one of the architects competing for the commision […]

## Yet another proof that primes are infinite

In CS131, we see the “Proof from the Book” due to Euclide that the number of prime numbers is infinite. Here is another favorite proof that is based on elementary facts. Suppose that is a list of all the primes. From what we have learnt about the sum of geometric progressions we know that for […]

## The densest subgraph problem with negative weights

Few days ago I uploaded on Arxiv our preprint “Novel Dense Subgraph Discovery Primitives: Risk Aversion and Exclusion Queries”. This is joint work with Tianyi, Nao, and Jakub. In this paper we study the following extension of the densest subgraph problem (DSP) that is known to be solvable exactly in polynomial time on graphs with […]