Jin-Yi Cai (Chinese: 蔡进一; born 1961) is a Chinese American mathematician and computer scientist. He is a professor of computer science, and also the Steenbock Professor of Mathematical Sciences[1] at the University of Wisconsin–Madison. His research is in theoretical computer science, especially computational complexity theory. In recent years he has concentrated on the classification of computational counting problems, especially counting graph homomorphisms, counting constraint satisfaction problems, and Holant problems as related to holographic algorithms.