I will introduce a new structure on (relative) Symplectic
Cohomology defined in terms of a PROP called the “Plumber’s PROP.”
This PROP consists of nodal Riemann surfaces, of all genera and
with multiple inputs and outputs, satisfying a condition...
The possibility that some of the black holes in the universe
have a non-stellar origin and that they play a significant role in
cosmology - including being some or all of the dark matter - is
both timely and intriguing. I will review the status of...
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...
I will discuss dilaton gravity with a sine potential, where
periodic shifts of the dilaton (that leave the potential invariant)
are treated as a redundancy. Most things I will say hold true for
generic periodic potentials, but the sine potential is...
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...
Galaxies are at the core of nearly all modern astrophysical
studies. They serve as essential cosmological probes, tracing the
structure of the universe, while also providing the stage on which
stars form and black holes grow. Despite their...
