New directions in homological algebra

Principal faculty advisor: Haynes Miller, MIT

Palestine faculty advisors:
Professor Khalid Adarbeh, An-Najah National University
Professor Reema Sbeih, Birzeit University

This project will explore one of several possible new directions in homological algebra, depending upon the interests of the students. The starting point is the study of cohomology of groups (going back to the 1930s). What if the word "group" is replaced by other algebraic structures (such as ring, or commutative algebra, or monoid). What is the analogous theory, and how do we compute it? There are actually two competing definitions of cohomology in these cases, and in this project we will compare them and try to find out when they agree.

Hadeel AbuTabeekh, An-Najah National University
Mohamed Damaj, Birzeit University
Nasief Khlaif, Birzeit University
Daishi Kiyohara, MIT
Kenta J Suzuki, MIT
Ali Tahbub, Birzeit University

top row: Kenta Suzuki, Haynes Miller, Nasief Khlaif
middle row: Hadeel AbuTabeekh, Ali Tahboub, Mohammad Damaj
bottom row: Daishi Kiyohara

This project led on to three separate research projects over the spring of 2022:
Quillen homology of Lie algebras
Hochschild systems and alternative algebras
Harrison homology and the Quillen homology of commutative monoids