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...
A symplectic embedding of a disjoint union of domains into a
symplectic manifold M is said to be of Kahler type (respectively
tame) if it is holomorphic with respect to some (not a priori
fixed) integrable complex structure on M which is compatible...
The quantum unique ergodicity conjecture of Rudnick and Sarnak
concerns the mass equidistribution in the large eigenvalue limit of
Laplacian eigenfunctions on negatively curved manifolds. This
conjecture has been resolved by Lindenstrauss when this...
Fast inward migration of planetary cores embedded in gaseous
disks is a common problem in the current planet formation paradigm.
Even though dust is ubiquitous in protoplanetary disks, its
dynamical role in the migration history of planetary embryos...
We discuss a one-phase degenerate free boundary problem which
arises from the minimization of the so-called Alt-Phillips
functional. We establish partial regularity results for the free
boundary and discuss the rigidity of global minimizers when...
I will discuss pointwise ergodic theory as it developed out of
Bourgain's work in the 80s, leading up to my work with Mirek and
Tao on bilinear ergodic averages.
