The cosmic microwave background is a sensitive probe of
early-Universe physics, and yet fundamental constants at
recombination can differ from their present day values due to
degeneracies in the standard cosmological model. Such scenarios
have been...
Symmetric power functoriality is one of the basic cases of
Langlands' functoriality conjectures and is the route to the proof
of the Sato-Tate conjecture (concerning the distribution of the
modulo p point counts of an elliptic curve over Q, as the...
A large toolbox of numerical schemes for dispersive equations
has been established, based on different discretization techniques
such as discretizing the variation-of-constants formula (e.g.,
exponential integrators) or splitting the full equation...
This talk is based on a joint work with Steve Lester.
We review the Gauss circle problem, and Hardy's conjecture
regarding the order of magnitude of the remainder term. It is
attempted to rigorously formulate the folklore heuristics behind
Hardy's...
Perhaps the most important problem in physics or quantum
chemistry is to determine properties of the ground state of an
interacting system of fermions. As a quantum mechanical
problem, there may be no efficient classical witness to the ground
state...
Ruzsa asked whether there exist Fourier-uniform subsets of ℤ/Nℤ
with very few 4-term arithmetic progressions (4-AP). The standard
pedagogical example of a Fourier uniform set with a "wrong" density
of 4-APs actually has 4-AP density much higher than...
In the last few years, expanders have been used in fast graph
algorithms in different models, including static, dynamic, and
distributed algorithms. I will survey these applications of
expanders, explain the expander-related tools behind this...
The CνB is a cosmological relic analogous to the CMB, and
contains information about the universe before it was
one-second-old. Reflection of relic neutrinos from the surface of
the Earth creates a significant local neutrino-antineutrino
asymmetry...
