Gabriel Angelini-Knoll: There is an active area of research on the frontier of two fields of mathematics: chromatic homotopy theory and algebraic K-theory. Chromatic homotopy theory organizes information about maps between spheres of varying dimensions into periodic families. Algebraic K-theory turns linear algebraic data into number theoretic and geometric information. In the late 1970's, F. Waldhausen envisioned that by combining these two fields one can shed light on high dimensional manifolds. In the early 2000's, Ch. Ausoni and J. Rognes generalized conjectures of S. Lichtenbaum and D. Quillen in number theory using the interaction between these two fields. My talk will survey these interesting interactions and describe my work in this area.