Algebraic complexity theory studies the complexity of fundamental computational problems within an algebraic framework of
computation. This includes the design and analysis of efficient algorithms for algebraic problems, a topic belonging to Computer Algebra. Algebraic Complexity adds to this
the quest for lower complexity bounds, an enterprise genuine to Theoretical Computer Science. The tools needed to establish such lower bounds cover a large spectrum of
mathematics: ranging from combinatorics to topology and algebraic geometry. In this sense, Algebraic Complexity Theory is a truly interdisciplinary project.