Higher Algebra and Arithmetic - Rothschild Lecture

Explore the concept of higher algebra and its implications for arithmetic in this Rothschild Lecture by Professor Lars Hesselholt. Delve into a fundamental reconsideration of natural numbers, examining how they can record not just the result of counting, but the process itself. Discover how this more basic notion of number forms the foundation for higher algebra, as developed by Joyal and Lurie. Investigate the potential for eliminating denominators in arithmetic, as advocated by Waldhausen, and learn about key manifestations of this approach, including topological cyclic homology and integral p-adic Hodge theory. Explore how these concepts impact areas such as arithmetic geometry and provide new insights into the Hasse-Weil zeta function. Gain a deeper understanding of how higher algebra is reshaping our approach to fundamental mathematical concepts and opening new avenues for research in number theory and related fields.