All AMMs are CFMMs. All DeFi Markets Have Invariants. A DeFi Market is Arbitrage-Free if and Only if it Has an Increasing Invariant

Explore a 46-minute lecture by Roger Lee from the University of Chicago as he presents groundbreaking research on decentralized finance markets at the Fields Institute Workshop on Decentralized Finance and Market Microstructure. Delve into the mathematical foundations of automated market makers (AMMs) and discover why all AMMs are constant function market makers (CFMMs), why all DeFi markets possess invariants, and the critical relationship between arbitrage-free markets and increasing invariants. This May 9, 2025 talk provides essential theoretical insights for understanding the mathematical structures underlying decentralized exchange mechanisms and their implications for market efficiency.