The Madsen-Tillmann spectrum is a concept in algebraic topology, specifically in the study of stable homotopy theory. It is named after mathematicians Madsen and Tillmann, who contributed to its development. This spectrum provides a framework for understanding the relationships between various topological spaces and their homotopy groups. In essence, the Madsen-Tillmann spectrum captures information about the stable homotopy type of certain spaces, particularly those related to configuration spaces of points in Euclidean space. It plays a significant role in connecting different areas of mathematics, including homotopy theory and algebraic geometry.