Fields Notes 18.1 - Page 19

PUBLIC LECTURE ADVENTURES in the th 7 dimension August 21, 2017 • Fields Institute Speaker: Jason Lotay (University College London) A lecture by acclaimed scholar Jason Lotay drew a large crowd at the University of Toronto Earth Sciences Centre Reichman Family Lecture Hall on August 21 to hear about Adventures in the 7th Dimension. Professor Lotay, a Reader in Mathematics at University College London, works on differential geometry, particularly geometry related with special holonomy and calibrated submanifolds, geometric flows including Lagrangian mean curvature flow, as well as instantons. He was an EPSRC Career Acceleration Fellow and held positions at Imperial College London, MSRI (Berkeley), and the University of Oxford. Lotay's lecture posited that special shapes, which exist in seven dimensions may help us to unlock the mysteries of the universe. It was a mathematical journey across multiple dimensions, which explored their role in art, science and popular culture. What is the 7th dimension? The idea of a dimension was introduced through the everyday act of buying furniture and further examples, with links to art, literature, popular culture and films. Along the way, the fundamental notion of symmetry was touched upon, as was the history of the study of higher dimensions. Why 7 dimensions? Important to Lotay's research is the idea of holonomy: a type of symmetry of curved objects, with connections to an exceptional mathematical structure that only exists in 7 dimensions. This exceptional holonomy is called G_2. What do we know about it? Holonomy G_2 was linked to soap bubbles, and so the important problem of trying to find these 7-dimensional objects was connected to the process of blowing a bubble and seeing it become round. This mechanism is closely related to the way heat dissipates, which is an extremely important equation in the study of thermodynamics. Lotay's research shows that this process can work to find 7-dimensional spaces with G_2 holonomy. The connection between the theory of soap bubbles and holonomy G_2 goes further, which was explained using shortest paths between points and how this relates to the geometry of a surface. What do we still want to find out? The ideas of String Theory and M-Theory were introduced, as ways to unite quantum theory and gravity (as described by General Relativity). This naturally led to higher dimensions and a link to holonomy G_2, which requires further exploration to answer some key questions. It is hoped that these answers may help to realize a Theory of Everything, and so help us to describe and understand our universe.  19