Tuesday, January 16, 2018 - 10:30am to 11:30am

Cockins Hall 240

**Title**: Distance matrices and quadratc embedding of graphs

**Speaker**: Nobuaki Obata (Tohoku University)

**Abstract**: A finite or infinite connected graph is said to be of QE class if it admits a quadratic embedding in an Euclidean or Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. As a quantitative approach, we introduce a new characteristic of a graph called the QE constant. We discuss some basic properties of QE constants, concrete examples and some questions relevant to the distance spectra.