Abstract: Point sets on the plane are a fundamental class of objects studied in discrete and computational geometry, with many applications in real life problems.
Abstract: We discuss Nielsen's result(1999) which characterizes pure state transformation under LOCC by connecting the quantum entanglement to the algebraic theory of majorization.
Abstract: The PCP theorem (AS,ALMSS 1991) guarantees that every NP language has a probabilistically checkable proof (PCP) system allowing a verifier to check a witness very efficiently using randomness, and allowing for small error.
Abstract: Assignment games with side payments are models of certain two-sided markets. It is known that prices which competitively balance supply and demand correspond to elements in the core.
Abstract: We will see an application of topology to prove combinatorial results. The Borsuk-Ulam theorem states that any continuous function f from the surface of the (n+1)-sphere to R^n should have a point x on the sphere such that f(x) = f(-x).
Abstract: While every win-lose two person extensive game with finitely many moves and finitely many actions in each move and with perfect information admits an optimal winning strategy, it can fail to be true once the number of moves is countable
