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