In this project, Kriz works in K-theory and related areas. For example, methods of Real K-theory, which he generalized to the subject of Real cobordism jointly with Po Hu, are receiving current attention because of their relevance in the recent solution of the famous Kervaire-Milnor problem by Hill, Hopkins and Ravenel. A part of this project is dedicated to investigating further questions arising from these developments. In another aspect of the project, Kriz investigates algebraic and Hermitian K-theory, following his recent joint paper with Hu and Ormsby solving the homotopy limit problem for algebraic Hermitian K-theory. This leads to new investigations in motivic homotopy theory.
The field investigated in this project is a part of algebraic topology, which plays a central role in contemporary mathematics: its methods are used in diverse fields from geometry and analysis to number theory and algebra. The field also has interdisciplinary application. It has become clear in recent years that algebraic topology, and specifically K-theory, on which this project focuses, are crucial tools of mathematical physics in its ongoing quest toward explaining the fundamental physical laws of our universe.
