Title: Graphs, curvature, and local discrepancySpeaker: Paul Horn Affiliation: University of Denver Location: contact Sabrina Lato for Zoom link
Abstract: Spectral graph theory, the use of eigenvalues to study graphs, gives an important window into many properties of graphs. One of the reasons for this is that the eigenvalues can be used to certify the `pseudo-randomness' of the edge set of a graph. In recent years, several notions of discrete curvature have been introduced that gives a 'local' way (depending on the neighborhood structure of vertices) to study some of the same properties that eigenvalues can capture.
Title: The Hat Guessing Number of GraphsSpeaker: Jeremy Chizewer Affiliation: University of Waterloo Location: MC 6029
Abstract: The hat guessing number HG(G) of a graph G on n vertices is defined in terms of the following game: n players are placed on the n vertices of G, each wearing a hat whose color is arbitrarily chosen from a set of q possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number HG(G) is the largest integer q such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of q possible colors.