K-theory and related topics

在这个项目中，Kriz研究的是k理论和相关领域。例如，他与Po Hu共同推广到实数协同问题的Real K-theory方法，由于与Hill、Hopkins和Ravenel最近解决的著名的Kervaire-Milnor问题的相关性而受到当前的关注。这个项目的一部分致力于调查这些发展所产生的进一步问题。在该项目的另一方面，Kriz研究了代数和厄米k理论，继他最近与Hu和Ormsby合作的论文解决了代数厄米k理论的同伦极限问题之后。这给动机同伦理论带来了新的研究。本项目研究的领域是代数拓扑的一部分，代数拓扑在当代数学中起着核心作用：它的方法被用于从几何和分析到数论和代数的各个领域。该领域也有跨学科的应用。近年来，越来越清楚的是，代数拓扑，特别是这个项目所关注的k理论，是数学物理学在解释宇宙基本物理定律的过程中至关重要的工具。

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.