Research in commutative and homological algebra at the mathematics department was initiated in the late 1960s by Jan-Erik Roos, Christer Lech and Jan-Erik Björk. They gradually built a strong group in this area including, in particular, C.Löfwall, R.Fröberg, Ch.Gottlieb, J.Backelin. Studies of algebraic and tropical  geometry, homotopy theory and operads were later strengthened by T.Ekedahl, M.Passare, and S.Merkulov. Some of the present research efforts in the group  may be regarded as a continuation of the activities of this internationally recognized research group.  At the same time new members of the group broaden the number of research directions  which now additionally include e.g. stable homotopy theory, moduli spaces, number theory, Langlands program, to mention a few.