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...
In a vertex expanding graph, every small subset of vertices
neighbors many different vertices. Random graphs are near-optimal
vertex expanders; however, it has proven difficult to create
families of deterministic near-optimal vertex expanders, as...
Supersymmetric black holes in Anti de-Sitter space have recently
been shown to have a large number of exactly degenerate
microstates. In the first part of the talk, we will review how AdS5
black hole microstates may be reliably counted in the dual N...
