The general Art Gallery Problem (AGP) consists in finding the minimum number of guards sufficient to ensure the visibility coverage of an art gallery represented by a polygon.

A randomized algorithm for approximating the volume of a convex body K in n-dimensional Euclidean space was proposed by Martin Dyer, Alan Frieze and Ravi Kannan in 1988.

We will talk about the notion of the sign-rank of a {-1, 1}-valued matrix, which measures the robustness of it's rank under sign preserving changes.  We will first see a neat geometric interpretation of the sign-rank, and then see how showing an u

Abstract: In 1853, Liouville proved a fundamental result concerning approximations of algebraic numbers by rationals, which said one can't approximate algebraic numbers "well" using rationals.

Abstract: The art gallery problem is a classical sensor placement problem that asks for the minimum number of guards required to see every point in an environment.