I will explain recent progress on computing approximate ground
states of mean-field spin glass Hamiltonians, which are certain
random functions in high dimension. While the asymptotic ground
state energy OPT is given by the famous Parisi formula...
A Diophantine upper bound on the dimensions of certain spaces of
holonomic functions was the main ingredient in our proof with
Calegari and Tang of the 'unbounded denominators conjecture'
(presented by Tang in last year's number theory seminar)
from...
Large-area surveys such as Gaia have given us an unprecedented
amount of data on stars in the Milky Way. One of the largest
ongoing challenges in understanding the present-day structure and
formation history of our Galaxy (i.e. Galactic archaeology)...
