In this talk, I will elaborate on the main technical component
of our PCP—the construction of routing protocols on
high-dimensional expanders (HDX) that can withstand a constant
fraction of edge corruptions. We consider the following routing
problem...
The theory of probabilistically checkable proofs (PCPs) shows
how to encode a proof for any theorem into a format where the
theorem's correctness can be verified by making only a constant
number of queries to the proof. The PCP Theorem [ALMSS] is a...
Recent progress on character bounds for groups of Lie type makes
it feasible in many cases to find the asymptotic growth, for fixed
q and n tending to infinity, of the number of n-dimensional
representations of a Fuchsian group G over the field with...
We show that two generic, open, convex or concave toric domains
in R4 are symplectomorphic if and only if they agree up to
reflection. The proof uses barcodes in positive S1-equivariant
symplectic homology, or equivalently in cylindrical contact...
In the 1940s Mahler initiated the program of determining the
bass note spectrum Spec(P):={infx⎯⎯∈Λ∖0⎯⎯∣∣P(x⎯⎯)∣∣,Λ⊂ℝk a
unimodular lattice} for some homogeneous form P. Understanding this
spectrum is central in the geometry of numbers and offers a...
For an embedded stable curve over the real numbers we introduce
a hyperplane arrangement in the tangent space of the Hilbert
scheme. The connected components of its complement are labeled by
embeddings of the graph of the stable curve to a compact...
Teichmuller dynamics give us a nonhomogeneous example of an
action of SL_2(R) on a space H_g preserving a finite measure. This
space is related to the moduli space of genus g curves. The SL_2(R)
action on H_g has a complicated behavior: McMullen...
In this talk, we will explore recent developments in the study
of coherent structures evolving by incompressible flows. Our focus
will be on the behavior of fluid interfaces and vortex filaments.
We include the dynamics of gravity Stokes interfaces...
Algebraic torsion is a means of understanding the topological
complexity of certain homomorphic curves counted in some Floer
theories of contact manifolds. This talk focuses on algebraic
torsion and the contact invariant in embedded contact...
