Fourteenth Annual R.A. Blyth Lectures in Mathematics
(Information on the Blyth Lectures is available on the index page)
Professor Scott Sheffield
Massachusetts Institute of Technology
Will give three lectures on Quantum Gravity and Randomized Space-Time Geometry
In general relativity the space-time geometry is not a flat four
dimensional space. It is curved ("warped") by the presence of matter
and energy in a manner described by Einstein. In quantum mechanics, the
density of matter and energy is, in a sense, random. A central goal of
modern physics is unify these theories into a single coherent framework.
This requires addressing the randomness of space-time itself.
This is no simple task. How does one even describe a universe in which
basic geometric properties (lengths, areas, directions of "straight"
lines, etc.) are uncertain? Put mathematically, what are the most
natural measures on the space of all geometries? And to what extent can
these measures be precisely understood in a mathematical way?
These lectures will address (with copious illustrations) a
two-dimensional version of these problems and a particular family of
random geometries called "Liouville quantum gravity", which have been a
starting point for more complicated constructions in string theory.
These lectures will not unify general relativity and quantum mechanics,
but they will least illustrate how mathematically subtle -- yet
beautiful -- random geometry can be.
The first talk will be accessible to a general scientific audience. The
second and third will be at the level of a colloquium for mathematicians
and physicists.
Mathematical keywords: Schramm-Loewner evolution, Riemann
uniformization, random planar maps, conformal welding, conformal field
theory, Gaussian free field.
Lecture 1:
Wednesday, April 1, 2009, 4:10 p.m.
Bahen Centre for Information Technology, 40 St. George St.
Room 1170
Lecture 2:
Thursday, April 2, 2009, 4:10 p.m.
Bahen Centre for Information Technology, 40 St. George St.
Room 1130
Lecture 3:
Friday, April 3, 2009, 4:10 p.m.
Bahen Centre for Information Technology, 40 St. George St.
Room 1130
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