M- and F-theory compactifications with ADE singularities give
rise to non-abelian ADE gauge symmetries. The physical explanation
for this phenomenon involves M2-branes wrapped on vanishing cycles.
We consider an alternative approach which relies on...
The Higgs mechanism is a part of the Standard Model of quantum
mechanics that allows certain kinds of particles to have nonzero
mass. In spite of its great importance, there is no rigorous proof
that the Higgs mechanism can indeed generate mass in...
Results concerning rigidity of Lagrangian submanifolds lie at
the heart of symplectic topology, and have been intensively studied
since the 1990s. An example for this phenomenon is the concept of
Lagrangian Barriers, a form of symplectic rigidity...
Strong spatial mixing (SSM) is an important and widely studied
quantitative notion of "correlation decay" for a variety of natural
distributions arising in statistical physics, probability theory,
and theoretical computer science. One of the most...
A smooth, oriented n-manifold is called a homotopy sphere if it
is homeomorphic, but not necessarily diffeomorphic, to the standard
n-sphere. In dimensions n>4
, one often studies the group Θn of homotopy spheres up to
orientation-preserving...
Given a grid diagram for a knot or link in the three-sphere, we
construct a spectrum whose homology is the knot Floer homology of .
We conjecture that the homotopy type of the spectrum is an
invariant of . Our construction does not use holomorphic...
In joint work in progress with Anschütz and Le Bras we aim to
construct a 6-functor formalism for quasicoherent sheaves on the
relative Fargues-Fontaine curve over rigid-analytic varieties (and
even general v-stacks), providing new insights into the...
The recent work of Drinfeld and Bhatt-Lurie led to a new
geometric approach to p-adic cohomology theories, analogously to
what was done earlier in Hodge theory by Simpson. This stacky
perspective gives in particular a new approach to p-adic non...
Despite the remarkable success of the standard model of
cosmology, the lambda CDM model, at predicting the observed
structure of the universe over many scales, very little is known
about the fundamental nature of its principal constituents:
dark...