Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds, and simultaneously dramatically extended our understanding of many infinite groups.

Short Biography: Daniel Wise grew up in New York and received his BA from Yeshiva University and his PhD from Princeton (1996). After stimulating postdocs and visiting positions at Berkeley, Cornell, and Brandeis, he moved to McGill in 2001, where he is a James McGill Professor. His primary research agenda has been to explore and promulgate the utility and ubiquity of non-positively curved cubical geometry in group theory and topology. He has received an AMS Veblen Prize, the CRM-Fields-PIMS Prize, a Guggenheim Fellowship, a Lobachevsky Medal, and is a Fellow of the Royal Society of London. Daniel Wise is currently on Sabbatical at the Weizmann Institute of Science in Israel.