Global symmetries are expected to be violated in quantum
gravity. The violation can be captured by nonzero scattering
amplitudes with different initial and final global charges. In this
talk, I will discuss such processes involving the scattering
of...
Following Birkhoff's proof of the Pointwise Ergodic Theorem, it
has been studied whether convergence still holds along various
subsequences. In 2020, Bergelson and Richter showed that under the
additional assumption of unique ergodicity, pointwise...
Can you hear the shape of LQG? We obtain a Weyl law for the
eigenvalues of Liouville Brownian motion: the n-th eigenvalue grows
linearly with n, with the proportionality constant given by the
Liouville area of the domain (times a certain...
The discovery of high-energy cosmic neutrinos opened a new
window of astroparticle physics. Their origin is a new mystery in
the field, which is tightly connected to the long-standing puzzle
about the origin of cosmic rays. I will discuss...
Graph Crossing Number is a fundamental and extensively studied
problem with wide ranging applications. In this problem, the goal
is to draw an input graph G in the plane so as to minimize the
number of crossings between the images of its edges. The...
Many cohomology theories in algebraic geometry, such as
crystalline and syntomic cohomology, are not homotopy invariant.
This is a shame, because it means that the stable motivic homotopy
theory of Morel--Voevodsky cannot be employed in studying
the...
Given a flow on a manifold, how to perturb it in order to create
a periodic orbit passing through a given region? While the first
results in this direction were obtained in the 1960-ies, various
facets of this question remain largely open. I will...
Determining the complexity of matrix multiplication is a
fundamental problem of theoretical computer science. It is
popularly conjectured that matrices can be multiplied in
nearly-linear time. If true, this conjecture would yield
similarly-fast...
Phenomena involving interactions of waves happen at different
scales and in different media: from gravitational waves to the
waves on the surface of the ocean, from our milk and coffee in the
morning to infinitesimal particles that behave like wave...
